1.1 --- a/doc-src/IsarRef/Thy/document/Proof.tex Sun Nov 07 23:32:26 2010 +0100
1.2 +++ b/doc-src/IsarRef/Thy/document/Proof.tex Mon Nov 08 00:00:47 2010 +0100
1.3 @@ -31,16 +31,16 @@
1.4
1.5 \begin{description}
1.6
1.7 - \item \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} means that a new goal has just been
1.8 + \item \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} means that a new goal has just been
1.9 stated that is now to be \emph{proven}; the next command may refine
1.10 it by some proof method, and enter a sub-proof to establish the
1.11 actual result.
1.12
1.13 - \item \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} is like a nested theory mode: the
1.14 + \item \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} is like a nested theory mode: the
1.15 context may be augmented by \emph{stating} additional assumptions,
1.16 intermediate results etc.
1.17
1.18 - \item \isa{{\isachardoublequote}proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} is intermediate between \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} and \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}}: existing facts (i.e.\
1.19 + \item \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} is intermediate between \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}: existing facts (i.e.\
1.20 the contents of the special ``\indexref{}{fact}{this}\hyperlink{fact.this}{\mbox{\isa{this}}}'' register) have been
1.21 just picked up in order to be used when refining the goal claimed
1.22 next.
1.23 @@ -71,17 +71,17 @@
1.24 %
1.25 \begin{isamarkuptext}%
1.26 \begin{matharray}{rcl}
1.27 - \indexdef{}{command}{example\_proof}\hypertarget{command.example-proof}{\hyperlink{command.example-proof}{\mbox{\isa{\isacommand{example{\isacharunderscore}proof}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
1.28 + \indexdef{}{command}{example\_proof}\hypertarget{command.example-proof}{\hyperlink{command.example-proof}{\mbox{\isa{\isacommand{example{\isaliteral{5F}{\isacharunderscore}}proof}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.29 \end{matharray}
1.30
1.31 \begin{description}
1.32
1.33 - \item \hyperlink{command.example-proof}{\mbox{\isa{\isacommand{example{\isacharunderscore}proof}}}} opens an empty proof body. This
1.34 + \item \hyperlink{command.example-proof}{\mbox{\isa{\isacommand{example{\isaliteral{5F}{\isacharunderscore}}proof}}}} opens an empty proof body. This
1.35 allows to experiment with Isar, without producing any persistent
1.36 result.
1.37
1.38 Structurally, this is like a vacous \hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}} statement
1.39 - followed by ``\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'', which means the
1.40 + followed by ``\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{22}{\isachardoublequote}}}'', which means the
1.41 example proof may be closed by a regular \hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}, or
1.42 discontinued by \hyperlink{command.oops}{\mbox{\isa{\isacommand{oops}}}}.
1.43
1.44 @@ -95,9 +95,9 @@
1.45 %
1.46 \begin{isamarkuptext}%
1.47 \begin{matharray}{rcl}
1.48 - \indexdef{}{command}{next}\hypertarget{command.next}{\hyperlink{command.next}{\mbox{\isa{\isacommand{next}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
1.49 - \indexdef{}{command}{\{}\hypertarget{command.braceleft}{\hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isacharbraceleft}}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
1.50 - \indexdef{}{command}{\}}\hypertarget{command.braceright}{\hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isacharbraceright}}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
1.51 + \indexdef{}{command}{next}\hypertarget{command.next}{\hyperlink{command.next}{\mbox{\isa{\isacommand{next}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.52 + \indexdef{}{command}{\{}\hypertarget{command.braceleft}{\hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isaliteral{7B}{\isacharbraceleft}}}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.53 + \indexdef{}{command}{\}}\hypertarget{command.braceright}{\hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isaliteral{7D}{\isacharbraceright}}}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.54 \end{matharray}
1.55
1.56 While Isar is inherently block-structured, opening and closing
1.57 @@ -119,9 +119,9 @@
1.58 \item \hyperlink{command.next}{\mbox{\isa{\isacommand{next}}}} switches to a fresh block within a
1.59 sub-proof, resetting the local context to the initial one.
1.60
1.61 - \item \hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isacharbraceleft}}}}} and \hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isacharbraceright}}}}} explicitly open and close
1.62 - blocks. Any current facts pass through ``\hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isacharbraceleft}}}}}''
1.63 - unchanged, while ``\hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isacharbraceright}}}}}'' causes any result to be
1.64 + \item \hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isaliteral{7B}{\isacharbraceleft}}}}}} and \hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isaliteral{7D}{\isacharbraceright}}}}}} explicitly open and close
1.65 + blocks. Any current facts pass through ``\hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isaliteral{7B}{\isacharbraceleft}}}}}}''
1.66 + unchanged, while ``\hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isaliteral{7D}{\isacharbraceright}}}}}}'' causes any result to be
1.67 \emph{exported} into the enclosing context. Thus fixed variables
1.68 are generalized, assumptions discharged, and local definitions
1.69 unfolded (cf.\ \secref{sec:proof-context}). There is no difference
1.70 @@ -139,7 +139,7 @@
1.71 %
1.72 \begin{isamarkuptext}%
1.73 \begin{matharray}{rcl}
1.74 - \indexdef{}{command}{oops}\hypertarget{command.oops}{\hyperlink{command.oops}{\mbox{\isa{\isacommand{oops}}}}} & : & \isa{{\isachardoublequote}proof\ {\isasymrightarrow}\ local{\isacharunderscore}theory\ {\isacharbar}\ theory{\isachardoublequote}} \\
1.75 + \indexdef{}{command}{oops}\hypertarget{command.oops}{\hyperlink{command.oops}{\mbox{\isa{\isacommand{oops}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{7C}{\isacharbar}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
1.76 \end{matharray}
1.77
1.78 The \hyperlink{command.oops}{\mbox{\isa{\isacommand{oops}}}} command discontinues the current proof
1.79 @@ -157,7 +157,7 @@
1.80 preparation tools of Isabelle described in \chref{ch:document-prep}.
1.81 Thus partial or even wrong proof attempts can be discussed in a
1.82 logically sound manner. Note that the Isabelle {\LaTeX} macros can
1.83 - be easily adapted to print something like ``\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}'' instead of
1.84 + be easily adapted to print something like ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}'' instead of
1.85 the keyword ``\hyperlink{command.oops}{\mbox{\isa{\isacommand{oops}}}}''.
1.86
1.87 \medskip The \hyperlink{command.oops}{\mbox{\isa{\isacommand{oops}}}} command is undo-able, unlike
1.88 @@ -176,10 +176,10 @@
1.89 %
1.90 \begin{isamarkuptext}%
1.91 \begin{matharray}{rcl}
1.92 - \indexdef{}{command}{fix}\hypertarget{command.fix}{\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
1.93 - \indexdef{}{command}{assume}\hypertarget{command.assume}{\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
1.94 - \indexdef{}{command}{presume}\hypertarget{command.presume}{\hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
1.95 - \indexdef{}{command}{def}\hypertarget{command.def}{\hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
1.96 + \indexdef{}{command}{fix}\hypertarget{command.fix}{\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.97 + \indexdef{}{command}{assume}\hypertarget{command.assume}{\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.98 + \indexdef{}{command}{presume}\hypertarget{command.presume}{\hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.99 + \indexdef{}{command}{def}\hypertarget{command.def}{\hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.100 \end{matharray}
1.101
1.102 The logical proof context consists of fixed variables and
1.103 @@ -188,16 +188,16 @@
1.104 logical framework. Introducing some \emph{arbitrary, but fixed}
1.105 variable via ``\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}'' results in a local value
1.106 that may be used in the subsequent proof as any other variable or
1.107 - constant. Furthermore, any result \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymphi}{\isacharbrackleft}x{\isacharbrackright}{\isachardoublequote}} exported from
1.108 + constant. Furthermore, any result \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} exported from
1.109 the context will be universally closed wrt.\ \isa{x} at the
1.110 - outermost level: \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymAnd}x{\isachardot}\ {\isasymphi}{\isacharbrackleft}x{\isacharbrackright}{\isachardoublequote}} (this is expressed in normal
1.111 + outermost level: \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} (this is expressed in normal
1.112 form using Isabelle's meta-variables).
1.113
1.114 - Similarly, introducing some assumption \isa{{\isasymchi}} has two effects.
1.115 + Similarly, introducing some assumption \isa{{\isaliteral{5C3C6368693E}{\isasymchi}}} has two effects.
1.116 On the one hand, a local theorem is created that may be used as a
1.117 fact in subsequent proof steps. On the other hand, any result
1.118 - \isa{{\isachardoublequote}{\isasymchi}\ {\isasymturnstile}\ {\isasymphi}{\isachardoublequote}} exported from the context becomes conditional wrt.\
1.119 - the assumption: \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymchi}\ {\isasymLongrightarrow}\ {\isasymphi}{\isachardoublequote}}. Thus, solving an enclosing goal
1.120 + \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6368693E}{\isasymchi}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} exported from the context becomes conditional wrt.\
1.121 + the assumption: \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C6368693E}{\isasymchi}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}}. Thus, solving an enclosing goal
1.122 using such a result would basically introduce a new subgoal stemming
1.123 from the assumption. How this situation is handled depends on the
1.124 version of assumption command used: while \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}
1.125 @@ -205,10 +205,10 @@
1.126 the goal, \hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}} leaves the subgoal unchanged in order
1.127 to be proved later by the user.
1.128
1.129 - Local definitions, introduced by ``\hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}~\isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}}'', are achieved by combining ``\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}'' with
1.130 + Local definitions, introduced by ``\hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}}'', are achieved by combining ``\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}'' with
1.131 another version of assumption that causes any hypothetical equation
1.132 - \isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}} to be eliminated by the reflexivity rule. Thus,
1.133 - exporting some result \isa{{\isachardoublequote}x\ {\isasymequiv}\ t\ {\isasymturnstile}\ {\isasymphi}{\isacharbrackleft}x{\isacharbrackright}{\isachardoublequote}} yields \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymphi}{\isacharbrackleft}t{\isacharbrackright}{\isachardoublequote}}.
1.134 + \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}} to be eliminated by the reflexivity rule. Thus,
1.135 + exporting some result \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} yields \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{5B}{\isacharbrackleft}}t{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}.
1.136
1.137 \begin{rail}
1.138 'fix' (vars + 'and')
1.139 @@ -225,21 +225,21 @@
1.140
1.141 \item \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x} introduces a local variable \isa{x} that is \emph{arbitrary, but fixed.}
1.142
1.143 - \item \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} and \hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} introduce a local fact \isa{{\isachardoublequote}{\isasymphi}\ {\isasymturnstile}\ {\isasymphi}{\isachardoublequote}} by
1.144 + \item \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} and \hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} introduce a local fact \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7068693E}{\isasymphi}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} by
1.145 assumption. Subsequent results applied to an enclosing goal (e.g.\
1.146 by \indexref{}{command}{show}\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}) are handled as follows: \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}} expects to be able to unify with existing premises in the
1.147 - goal, while \hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}} leaves \isa{{\isasymphi}} as new subgoals.
1.148 + goal, while \hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}} leaves \isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} as new subgoals.
1.149
1.150 Several lists of assumptions may be given (separated by
1.151 \indexref{}{keyword}{and}\hyperlink{keyword.and}{\mbox{\isa{\isakeyword{and}}}}; the resulting list of current facts consists
1.152 of all of these concatenated.
1.153
1.154 - \item \hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}~\isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}} introduces a local
1.155 + \item \hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}} introduces a local
1.156 (non-polymorphic) definition. In results exported from the context,
1.157 - \isa{x} is replaced by \isa{t}. Basically, ``\hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}~\isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}}'' abbreviates ``\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}}'', with the resulting
1.158 + \isa{x} is replaced by \isa{t}. Basically, ``\hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}}'' abbreviates ``\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}}'', with the resulting
1.159 hypothetical equation solved by reflexivity.
1.160
1.161 - The default name for the definitional equation is \isa{x{\isacharunderscore}def}.
1.162 + The default name for the definitional equation is \isa{x{\isaliteral{5F}{\isacharunderscore}}def}.
1.163 Several simultaneous definitions may be given at the same time.
1.164
1.165 \end{description}
1.166 @@ -256,15 +256,15 @@
1.167 %
1.168 \begin{isamarkuptext}%
1.169 \begin{matharray}{rcl}
1.170 - \indexdef{}{command}{let}\hypertarget{command.let}{\hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
1.171 + \indexdef{}{command}{let}\hypertarget{command.let}{\hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.172 \indexdef{}{keyword}{is}\hypertarget{keyword.is}{\hyperlink{keyword.is}{\mbox{\isa{\isakeyword{is}}}}} & : & syntax \\
1.173 \end{matharray}
1.174
1.175 - Abbreviations may be either bound by explicit \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}~\isa{{\isachardoublequote}p\ {\isasymequiv}\ t{\isachardoublequote}} statements, or by annotating assumptions or
1.176 - goal statements with a list of patterns ``\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIS}\ p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub n{\isacharparenright}{\isachardoublequote}}''. In both cases, higher-order matching is invoked to
1.177 + Abbreviations may be either bound by explicit \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}p\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}} statements, or by annotating assumptions or
1.178 + goal statements with a list of patterns ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C49533E}{\isasymIS}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}''. In both cases, higher-order matching is invoked to
1.179 bind extra-logical term variables, which may be either named
1.180 - schematic variables of the form \isa{{\isacharquery}x}, or nameless dummies
1.181 - ``\hyperlink{variable.underscore}{\mbox{\isa{{\isacharunderscore}}}}'' (underscore). Note that in the \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}
1.182 + schematic variables of the form \isa{{\isaliteral{3F}{\isacharquery}}x}, or nameless dummies
1.183 + ``\hyperlink{variable.underscore}{\mbox{\isa{{\isaliteral{5F}{\isacharunderscore}}}}}'' (underscore). Note that in the \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}
1.184 form the patterns occur on the left-hand side, while the \hyperlink{keyword.is}{\mbox{\isa{\isakeyword{is}}}} patterns are in postfix position.
1.185
1.186 Polymorphism of term bindings is handled in Hindley-Milner style,
1.187 @@ -292,12 +292,12 @@
1.188
1.189 \begin{description}
1.190
1.191 - \item \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}~\isa{{\isachardoublequote}p\isactrlsub {\isadigit{1}}\ {\isacharequal}\ t\isactrlsub {\isadigit{1}}\ {\isasymAND}\ {\isasymdots}\ p\isactrlsub n\ {\isacharequal}\ t\isactrlsub n{\isachardoublequote}} binds any
1.192 - text variables in patterns \isa{{\isachardoublequote}p\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ p\isactrlsub n{\isachardoublequote}} by simultaneous
1.193 - higher-order matching against terms \isa{{\isachardoublequote}t\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ t\isactrlsub n{\isachardoublequote}}.
1.194 + \item \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}p\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3D}{\isacharequal}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} binds any
1.195 + text variables in patterns \isa{{\isaliteral{22}{\isachardoublequote}}p\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} by simultaneous
1.196 + higher-order matching against terms \isa{{\isaliteral{22}{\isachardoublequote}}t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}.
1.197
1.198 - \item \isa{{\isachardoublequote}{\isacharparenleft}{\isasymIS}\ p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub n{\isacharparenright}{\isachardoublequote}} resembles \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}, but
1.199 - matches \isa{{\isachardoublequote}p\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ p\isactrlsub n{\isachardoublequote}} against the preceding statement. Also
1.200 + \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C49533E}{\isasymIS}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} resembles \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}, but
1.201 + matches \isa{{\isaliteral{22}{\isachardoublequote}}p\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} against the preceding statement. Also
1.202 note that \hyperlink{keyword.is}{\mbox{\isa{\isakeyword{is}}}} is not a separate command, but part of
1.203 others (such as \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}, \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}} etc.).
1.204
1.205 @@ -309,8 +309,8 @@
1.206 abstracted over any meta-level parameters (if present). Likewise,
1.207 \indexref{}{variable}{this}\hyperlink{variable.this}{\mbox{\isa{this}}} is bound for fact statements resulting from
1.208 assumptions or finished goals. In case \hyperlink{variable.this}{\mbox{\isa{this}}} refers to
1.209 - an object-logic statement that is an application \isa{{\isachardoublequote}f\ t{\isachardoublequote}}, then
1.210 - \isa{t} is bound to the special text variable ``\hyperlink{variable.dots}{\mbox{\isa{{\isasymdots}}}}''
1.211 + an object-logic statement that is an application \isa{{\isaliteral{22}{\isachardoublequote}}f\ t{\isaliteral{22}{\isachardoublequote}}}, then
1.212 + \isa{t} is bound to the special text variable ``\hyperlink{variable.dots}{\mbox{\isa{{\isaliteral{5C3C646F74733E}{\isasymdots}}}}}''
1.213 (three dots). The canonical application of this convenience are
1.214 calculational proofs (see \secref{sec:calculation}).%
1.215 \end{isamarkuptext}%
1.216 @@ -322,12 +322,12 @@
1.217 %
1.218 \begin{isamarkuptext}%
1.219 \begin{matharray}{rcl}
1.220 - \indexdef{}{command}{note}\hypertarget{command.note}{\hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
1.221 - \indexdef{}{command}{then}\hypertarget{command.then}{\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} \\
1.222 - \indexdef{}{command}{from}\hypertarget{command.from}{\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} \\
1.223 - \indexdef{}{command}{with}\hypertarget{command.with}{\hyperlink{command.with}{\mbox{\isa{\isacommand{with}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} \\
1.224 - \indexdef{}{command}{using}\hypertarget{command.using}{\hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
1.225 - \indexdef{}{command}{unfolding}\hypertarget{command.unfolding}{\hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
1.226 + \indexdef{}{command}{note}\hypertarget{command.note}{\hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.227 + \indexdef{}{command}{then}\hypertarget{command.then}{\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.228 + \indexdef{}{command}{from}\hypertarget{command.from}{\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.229 + \indexdef{}{command}{with}\hypertarget{command.with}{\hyperlink{command.with}{\mbox{\isa{\isacommand{with}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.230 + \indexdef{}{command}{using}\hypertarget{command.using}{\hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.231 + \indexdef{}{command}{unfolding}\hypertarget{command.unfolding}{\hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.232 \end{matharray}
1.233
1.234 New facts are established either by assumption or proof of local
1.235 @@ -350,8 +350,8 @@
1.236
1.237 \begin{description}
1.238
1.239 - \item \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isachardoublequote}a\ {\isacharequal}\ b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}} recalls existing facts
1.240 - \isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ b\isactrlsub n{\isachardoublequote}}, binding the result as \isa{a}. Note that
1.241 + \item \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{3D}{\isacharequal}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} recalls existing facts
1.242 + \isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}, binding the result as \isa{a}. Note that
1.243 attributes may be involved as well, both on the left and right hand
1.244 sides.
1.245
1.246 @@ -368,30 +368,30 @@
1.247 \item \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{b} abbreviates ``\hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{b}~\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}''; thus \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}} is
1.248 equivalent to ``\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{this}''.
1.249
1.250 - \item \hyperlink{command.with}{\mbox{\isa{\isacommand{with}}}}~\isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}} abbreviates ``\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n\ {\isasymAND}\ this{\isachardoublequote}}''; thus the forward chaining
1.251 + \item \hyperlink{command.with}{\mbox{\isa{\isacommand{with}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} abbreviates ``\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ this{\isaliteral{22}{\isachardoublequote}}}''; thus the forward chaining
1.252 is from earlier facts together with the current ones.
1.253
1.254 - \item \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}} augments the facts being
1.255 + \item \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} augments the facts being
1.256 currently indicated for use by a subsequent refinement step (such as
1.257 \indexref{}{command}{apply}\hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}} or \indexref{}{command}{proof}\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}).
1.258
1.259 - \item \hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}}~\isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}} is structurally
1.260 + \item \hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} is structurally
1.261 similar to \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}, but unfolds definitional equations
1.262 - \isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}} throughout the goal state and facts.
1.263 + \isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} throughout the goal state and facts.
1.264
1.265 \end{description}
1.266
1.267 Forward chaining with an empty list of theorems is the same as not
1.268 chaining at all. Thus ``\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{nothing}'' has no
1.269 - effect apart from entering \isa{{\isachardoublequote}prove{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} mode, since
1.270 + effect apart from entering \isa{{\isaliteral{22}{\isachardoublequote}}prove{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} mode, since
1.271 \indexref{}{fact}{nothing}\hyperlink{fact.nothing}{\mbox{\isa{nothing}}} is bound to the empty list of theorems.
1.272
1.273 Basic proof methods (such as \indexref{}{method}{rule}\hyperlink{method.rule}{\mbox{\isa{rule}}}) expect multiple
1.274 facts to be given in their proper order, corresponding to a prefix
1.275 of the premises of the rule involved. Note that positions may be
1.276 - easily skipped using something like \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{{\isachardoublequote}{\isacharunderscore}\ {\isasymAND}\ a\ {\isasymAND}\ b{\isachardoublequote}}, for example. This involves the trivial rule
1.277 - \isa{{\isachardoublequote}PROP\ {\isasympsi}\ {\isasymLongrightarrow}\ PROP\ {\isasympsi}{\isachardoublequote}}, which is bound in Isabelle/Pure as
1.278 - ``\indexref{}{fact}{\_}\hyperlink{fact.underscore}{\mbox{\isa{{\isacharunderscore}}}}'' (underscore).
1.279 + easily skipped using something like \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ a\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ b{\isaliteral{22}{\isachardoublequote}}}, for example. This involves the trivial rule
1.280 + \isa{{\isaliteral{22}{\isachardoublequote}}PROP\ {\isaliteral{5C3C7073693E}{\isasympsi}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ PROP\ {\isaliteral{5C3C7073693E}{\isasympsi}}{\isaliteral{22}{\isachardoublequote}}}, which is bound in Isabelle/Pure as
1.281 + ``\indexref{}{fact}{\_}\hyperlink{fact.underscore}{\mbox{\isa{{\isaliteral{5F}{\isacharunderscore}}}}}'' (underscore).
1.282
1.283 Automated methods (such as \hyperlink{method.simp}{\mbox{\isa{simp}}} or \hyperlink{method.auto}{\mbox{\isa{auto}}}) just
1.284 insert any given facts before their usual operation. Depending on
1.285 @@ -406,17 +406,17 @@
1.286 %
1.287 \begin{isamarkuptext}%
1.288 \begin{matharray}{rcl}
1.289 - \indexdef{}{command}{lemma}\hypertarget{command.lemma}{\hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
1.290 - \indexdef{}{command}{theorem}\hypertarget{command.theorem}{\hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
1.291 - \indexdef{}{command}{corollary}\hypertarget{command.corollary}{\hyperlink{command.corollary}{\mbox{\isa{\isacommand{corollary}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
1.292 - \indexdef{}{command}{schematic\_lemma}\hypertarget{command.schematic-lemma}{\hyperlink{command.schematic-lemma}{\mbox{\isa{\isacommand{schematic{\isacharunderscore}lemma}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
1.293 - \indexdef{}{command}{schematic\_theorem}\hypertarget{command.schematic-theorem}{\hyperlink{command.schematic-theorem}{\mbox{\isa{\isacommand{schematic{\isacharunderscore}theorem}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
1.294 - \indexdef{}{command}{schematic\_corollary}\hypertarget{command.schematic-corollary}{\hyperlink{command.schematic-corollary}{\mbox{\isa{\isacommand{schematic{\isacharunderscore}corollary}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
1.295 - \indexdef{}{command}{have}\hypertarget{command.have}{\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ proof{\isacharparenleft}chain{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
1.296 - \indexdef{}{command}{show}\hypertarget{command.show}{\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ proof{\isacharparenleft}chain{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
1.297 - \indexdef{}{command}{hence}\hypertarget{command.hence}{\hyperlink{command.hence}{\mbox{\isa{\isacommand{hence}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
1.298 - \indexdef{}{command}{thus}\hypertarget{command.thus}{\hyperlink{command.thus}{\mbox{\isa{\isacommand{thus}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
1.299 - \indexdef{}{command}{print\_statement}\hypertarget{command.print-statement}{\hyperlink{command.print-statement}{\mbox{\isa{\isacommand{print{\isacharunderscore}statement}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
1.300 + \indexdef{}{command}{lemma}\hypertarget{command.lemma}{\hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.301 + \indexdef{}{command}{theorem}\hypertarget{command.theorem}{\hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.302 + \indexdef{}{command}{corollary}\hypertarget{command.corollary}{\hyperlink{command.corollary}{\mbox{\isa{\isacommand{corollary}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.303 + \indexdef{}{command}{schematic\_lemma}\hypertarget{command.schematic-lemma}{\hyperlink{command.schematic-lemma}{\mbox{\isa{\isacommand{schematic{\isaliteral{5F}{\isacharunderscore}}lemma}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.304 + \indexdef{}{command}{schematic\_theorem}\hypertarget{command.schematic-theorem}{\hyperlink{command.schematic-theorem}{\mbox{\isa{\isacommand{schematic{\isaliteral{5F}{\isacharunderscore}}theorem}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.305 + \indexdef{}{command}{schematic\_corollary}\hypertarget{command.schematic-corollary}{\hyperlink{command.schematic-corollary}{\mbox{\isa{\isacommand{schematic{\isaliteral{5F}{\isacharunderscore}}corollary}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.306 + \indexdef{}{command}{have}\hypertarget{command.have}{\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.307 + \indexdef{}{command}{show}\hypertarget{command.show}{\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.308 + \indexdef{}{command}{hence}\hypertarget{command.hence}{\hyperlink{command.hence}{\mbox{\isa{\isacommand{hence}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.309 + \indexdef{}{command}{thus}\hypertarget{command.thus}{\hyperlink{command.thus}{\mbox{\isa{\isacommand{thus}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.310 + \indexdef{}{command}{print\_statement}\hypertarget{command.print-statement}{\hyperlink{command.print-statement}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}statement}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
1.311 \end{matharray}
1.312
1.313 From a theory context, proof mode is entered by an initial goal
1.314 @@ -429,7 +429,7 @@
1.315
1.316 Goals may consist of multiple statements, resulting in a list of
1.317 facts eventually. A pending multi-goal is internally represented as
1.318 - a meta-level conjunction (\isa{{\isachardoublequote}{\isacharampersand}{\isacharampersand}{\isacharampersand}{\isachardoublequote}}), which is usually
1.319 + a meta-level conjunction (\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}{\isaliteral{22}{\isachardoublequote}}}), which is usually
1.320 split into the corresponding number of sub-goals prior to an initial
1.321 method application, via \indexref{}{command}{proof}\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}
1.322 (\secref{sec:proof-steps}) or \indexref{}{command}{apply}\hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}
1.323 @@ -472,19 +472,19 @@
1.324
1.325 \begin{description}
1.326
1.327 - \item \hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} enters proof mode with
1.328 - \isa{{\isasymphi}} as main goal, eventually resulting in some fact \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymphi}{\isachardoublequote}} to be put back into the target context. An additional
1.329 + \item \hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} enters proof mode with
1.330 + \isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} as main goal, eventually resulting in some fact \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} to be put back into the target context. An additional
1.331 \railnonterm{context} specification may build up an initial proof
1.332 context for the subsequent claim; this includes local definitions
1.333 and syntax as well, see the definition of \hyperlink{syntax.contextelem}{\mbox{\isa{contextelem}}} in
1.334 \secref{sec:locale}.
1.335
1.336 - \item \hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} and \hyperlink{command.corollary}{\mbox{\isa{\isacommand{corollary}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} are essentially the same as \hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}}, but the facts are internally marked as
1.337 + \item \hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} and \hyperlink{command.corollary}{\mbox{\isa{\isacommand{corollary}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} are essentially the same as \hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}}, but the facts are internally marked as
1.338 being of a different kind. This discrimination acts like a formal
1.339 comment.
1.340
1.341 - \item \hyperlink{command.schematic-lemma}{\mbox{\isa{\isacommand{schematic{\isacharunderscore}lemma}}}}, \hyperlink{command.schematic-theorem}{\mbox{\isa{\isacommand{schematic{\isacharunderscore}theorem}}}},
1.342 - \hyperlink{command.schematic-corollary}{\mbox{\isa{\isacommand{schematic{\isacharunderscore}corollary}}}} are similar to \hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}},
1.343 + \item \hyperlink{command.schematic-lemma}{\mbox{\isa{\isacommand{schematic{\isaliteral{5F}{\isacharunderscore}}lemma}}}}, \hyperlink{command.schematic-theorem}{\mbox{\isa{\isacommand{schematic{\isaliteral{5F}{\isacharunderscore}}theorem}}}},
1.344 + \hyperlink{command.schematic-corollary}{\mbox{\isa{\isacommand{schematic{\isaliteral{5F}{\isacharunderscore}}corollary}}}} are similar to \hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}},
1.345 \hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}, \hyperlink{command.corollary}{\mbox{\isa{\isacommand{corollary}}}}, respectively but allow
1.346 the statement to contain unbound schematic variables.
1.347
1.348 @@ -495,14 +495,14 @@
1.349 proofs is lost, which also impacts performance, because proof
1.350 checking is forced into sequential mode.
1.351
1.352 - \item \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} claims a local goal,
1.353 + \item \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} claims a local goal,
1.354 eventually resulting in a fact within the current logical context.
1.355 This operation is completely independent of any pending sub-goals of
1.356 an enclosing goal statements, so \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}} may be freely
1.357 used for experimental exploration of potential results within a
1.358 proof body.
1.359
1.360 - \item \hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} is like \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} plus a second stage to refine some pending
1.361 + \item \hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} is like \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} plus a second stage to refine some pending
1.362 sub-goal for each one of the finished result, after having been
1.363 exported into the corresponding context (at the head of the
1.364 sub-proof of this \hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}} command).
1.365 @@ -525,14 +525,14 @@
1.366 \item \hyperlink{command.thus}{\mbox{\isa{\isacommand{thus}}}} abbreviates ``\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}~\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}''. Note that \hyperlink{command.thus}{\mbox{\isa{\isacommand{thus}}}} is also equivalent to
1.367 ``\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{this}~\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}''.
1.368
1.369 - \item \hyperlink{command.print-statement}{\mbox{\isa{\isacommand{print{\isacharunderscore}statement}}}}~\isa{a} prints facts from the
1.370 + \item \hyperlink{command.print-statement}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}statement}}}}~\isa{a} prints facts from the
1.371 current theory or proof context in long statement form, according to
1.372 the syntax for \hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}} given above.
1.373
1.374 \end{description}
1.375
1.376 Any goal statement causes some term abbreviations (such as
1.377 - \indexref{}{variable}{?thesis}\hyperlink{variable.?thesis}{\mbox{\isa{{\isacharquery}thesis}}}) to be bound automatically, see also
1.378 + \indexref{}{variable}{?thesis}\hyperlink{variable.?thesis}{\mbox{\isa{{\isaliteral{3F}{\isacharquery}}thesis}}}) to be bound automatically, see also
1.379 \secref{sec:term-abbrev}.
1.380
1.381 The optional case names of \indexref{}{element}{obtains}\hyperlink{element.obtains}{\mbox{\isa{\isakeyword{obtains}}}} have a twofold
1.382 @@ -556,7 +556,7 @@
1.383 methods via ``\verb|,|'' (sequential composition),
1.384 ``\verb||\verb,|,\verb||'' (alternative choices), ``\verb|?|''
1.385 (try), ``\verb|+|'' (repeat at least once), ``\verb|[|\isa{n}\verb|]|'' (restriction to first \isa{n}
1.386 - sub-goals, with default \isa{{\isachardoublequote}n\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequote}}). In practice, proof
1.387 + sub-goals, with default \isa{{\isaliteral{22}{\isachardoublequote}}n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}). In practice, proof
1.388 methods are usually just a comma separated list of
1.389 \railqtok{nameref}~\railnonterm{args} specifications. Note that
1.390 parentheses may be dropped for single method specifications (with no
1.391 @@ -572,18 +572,18 @@
1.392
1.393 Proper Isar proof methods do \emph{not} admit arbitrary goal
1.394 addressing, but refer either to the first sub-goal or all sub-goals
1.395 - uniformly. The goal restriction operator ``\isa{{\isachardoublequote}{\isacharbrackleft}n{\isacharbrackright}{\isachardoublequote}}''
1.396 + uniformly. The goal restriction operator ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}''
1.397 evaluates a method expression within a sandbox consisting of the
1.398 first \isa{n} sub-goals (which need to exist). For example, the
1.399 - method ``\isa{{\isachardoublequote}simp{\isacharunderscore}all{\isacharbrackleft}{\isadigit{3}}{\isacharbrackright}{\isachardoublequote}}'' simplifies the first three
1.400 - sub-goals, while ``\isa{{\isachardoublequote}{\isacharparenleft}rule\ foo{\isacharcomma}\ simp{\isacharunderscore}all{\isacharparenright}{\isacharbrackleft}{\isacharbrackright}{\isachardoublequote}}'' simplifies all
1.401 - new goals that emerge from applying rule \isa{{\isachardoublequote}foo{\isachardoublequote}} to the
1.402 + method ``\isa{{\isaliteral{22}{\isachardoublequote}}simp{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{3}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}'' simplifies the first three
1.403 + sub-goals, while ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}rule\ foo{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{29}{\isacharparenright}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}'' simplifies all
1.404 + new goals that emerge from applying rule \isa{{\isaliteral{22}{\isachardoublequote}}foo{\isaliteral{22}{\isachardoublequote}}} to the
1.405 originally first one.
1.406
1.407 Improper methods, notably tactic emulations, offer a separate
1.408 low-level goal addressing scheme as explicit argument to the
1.409 - individual tactic being involved. Here ``\isa{{\isachardoublequote}{\isacharbrackleft}{\isacharbang}{\isacharbrackright}{\isachardoublequote}}'' refers to
1.410 - all goals, and ``\isa{{\isachardoublequote}{\isacharbrackleft}n{\isacharminus}{\isacharbrackright}{\isachardoublequote}}'' to all goals starting from \isa{{\isachardoublequote}n{\isachardoublequote}}.
1.411 + individual tactic being involved. Here ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{21}{\isacharbang}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}'' refers to
1.412 + all goals, and ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}n{\isaliteral{2D}{\isacharminus}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}'' to all goals starting from \isa{{\isaliteral{22}{\isachardoublequote}}n{\isaliteral{22}{\isachardoublequote}}}.
1.413
1.414 \indexouternonterm{goalspec}
1.415 \begin{rail}
1.416 @@ -599,12 +599,12 @@
1.417 %
1.418 \begin{isamarkuptext}%
1.419 \begin{matharray}{rcl}
1.420 - \indexdef{}{command}{proof}\hypertarget{command.proof}{\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
1.421 - \indexdef{}{command}{qed}\hypertarget{command.qed}{\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ local{\isacharunderscore}theory\ {\isacharbar}\ theory{\isachardoublequote}} \\
1.422 - \indexdef{}{command}{by}\hypertarget{command.by}{\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ local{\isacharunderscore}theory\ {\isacharbar}\ theory{\isachardoublequote}} \\
1.423 - \indexdef{}{command}{..}\hypertarget{command.ddot}{\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ local{\isacharunderscore}theory\ {\isacharbar}\ theory{\isachardoublequote}} \\
1.424 - \indexdef{}{command}{.}\hypertarget{command.dot}{\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isachardot}}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ local{\isacharunderscore}theory\ {\isacharbar}\ theory{\isachardoublequote}} \\
1.425 - \indexdef{}{command}{sorry}\hypertarget{command.sorry}{\hyperlink{command.sorry}{\mbox{\isa{\isacommand{sorry}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ local{\isacharunderscore}theory\ {\isacharbar}\ theory{\isachardoublequote}} \\
1.426 + \indexdef{}{command}{proof}\hypertarget{command.proof}{\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.427 + \indexdef{}{command}{qed}\hypertarget{command.qed}{\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{7C}{\isacharbar}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
1.428 + \indexdef{}{command}{by}\hypertarget{command.by}{\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{7C}{\isacharbar}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
1.429 + \indexdef{}{command}{..}\hypertarget{command.ddot}{\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{7C}{\isacharbar}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
1.430 + \indexdef{}{command}{.}\hypertarget{command.dot}{\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{7C}{\isacharbar}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
1.431 + \indexdef{}{command}{sorry}\hypertarget{command.sorry}{\hyperlink{command.sorry}{\mbox{\isa{\isacommand{sorry}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{7C}{\isacharbar}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
1.432 \end{matharray}
1.433
1.434 Arbitrary goal refinement via tactics is considered harmful.
1.435 @@ -613,12 +613,12 @@
1.436
1.437 \begin{enumerate}
1.438
1.439 - \item An \emph{initial} refinement step \indexref{}{command}{proof}\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}} reduces a newly stated goal to a number
1.440 + \item An \emph{initial} refinement step \indexref{}{command}{proof}\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} reduces a newly stated goal to a number
1.441 of sub-goals that are to be solved later. Facts are passed to
1.442 - \isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}} for forward chaining, if so indicated by \isa{{\isachardoublequote}proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} mode.
1.443 + \isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} for forward chaining, if so indicated by \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} mode.
1.444
1.445 - \item A \emph{terminal} conclusion step \indexref{}{command}{qed}\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}} is intended to solve remaining goals. No facts are
1.446 - passed to \isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}}.
1.447 + \item A \emph{terminal} conclusion step \indexref{}{command}{qed}\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} is intended to solve remaining goals. No facts are
1.448 + passed to \isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}}.
1.449
1.450 \end{enumerate}
1.451
1.452 @@ -654,15 +654,15 @@
1.453
1.454 \begin{description}
1.455
1.456 - \item \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}} refines the goal by proof
1.457 - method \isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}}; facts for forward chaining are passed if so
1.458 - indicated by \isa{{\isachardoublequote}proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} mode.
1.459 + \item \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} refines the goal by proof
1.460 + method \isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}; facts for forward chaining are passed if so
1.461 + indicated by \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} mode.
1.462
1.463 - \item \hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}} refines any remaining goals by
1.464 - proof method \isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}} and concludes the sub-proof by assumption.
1.465 - If the goal had been \isa{{\isachardoublequote}show{\isachardoublequote}} (or \isa{{\isachardoublequote}thus{\isachardoublequote}}), some
1.466 + \item \hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} refines any remaining goals by
1.467 + proof method \isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} and concludes the sub-proof by assumption.
1.468 + If the goal had been \isa{{\isaliteral{22}{\isachardoublequote}}show{\isaliteral{22}{\isachardoublequote}}} (or \isa{{\isaliteral{22}{\isachardoublequote}}thus{\isaliteral{22}{\isachardoublequote}}}), some
1.469 pending sub-goal is solved as well by the rule resulting from the
1.470 - result \emph{exported} into the enclosing goal context. Thus \isa{{\isachardoublequote}qed{\isachardoublequote}} may fail for two reasons: either \isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}} fails, or the
1.471 + result \emph{exported} into the enclosing goal context. Thus \isa{{\isaliteral{22}{\isachardoublequote}}qed{\isaliteral{22}{\isachardoublequote}}} may fail for two reasons: either \isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} fails, or the
1.472 resulting rule does not fit to any pending goal\footnote{This
1.473 includes any additional ``strong'' assumptions as introduced by
1.474 \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}.} of the enclosing context. Debugging such a
1.475 @@ -670,25 +670,25 @@
1.476 \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}, or weakening the local context by replacing
1.477 occurrences of \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}} by \hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}}.
1.478
1.479 - \item \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}\ m\isactrlsub {\isadigit{2}}{\isachardoublequote}} is a \emph{terminal
1.480 - proof}\index{proof!terminal}; it abbreviates \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}}~\isa{{\isachardoublequote}qed{\isachardoublequote}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}}, but with
1.481 + \item \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} is a \emph{terminal
1.482 + proof}\index{proof!terminal}; it abbreviates \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}~\isa{{\isaliteral{22}{\isachardoublequote}}qed{\isaliteral{22}{\isachardoublequote}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}}, but with
1.483 backtracking across both methods. Debugging an unsuccessful
1.484 - \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}\ m\isactrlsub {\isadigit{2}}{\isachardoublequote}} command can be done by expanding its
1.485 - definition; in many cases \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}} (or even
1.486 - \isa{{\isachardoublequote}apply{\isachardoublequote}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}}) is already sufficient to see the
1.487 + \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} command can be done by expanding its
1.488 + definition; in many cases \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} (or even
1.489 + \isa{{\isaliteral{22}{\isachardoublequote}}apply{\isaliteral{22}{\isachardoublequote}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}) is already sufficient to see the
1.490 problem.
1.491
1.492 - \item ``\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}}'' is a \emph{default
1.493 - proof}\index{proof!default}; it abbreviates \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isachardoublequote}rule{\isachardoublequote}}.
1.494 + \item ``\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}}}}'' is a \emph{default
1.495 + proof}\index{proof!default}; it abbreviates \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}rule{\isaliteral{22}{\isachardoublequote}}}.
1.496
1.497 - \item ``\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isachardot}}}}}'' is a \emph{trivial
1.498 - proof}\index{proof!trivial}; it abbreviates \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isachardoublequote}this{\isachardoublequote}}.
1.499 + \item ``\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}}}}}'' is a \emph{trivial
1.500 + proof}\index{proof!trivial}; it abbreviates \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}this{\isaliteral{22}{\isachardoublequote}}}.
1.501
1.502 \item \hyperlink{command.sorry}{\mbox{\isa{\isacommand{sorry}}}} is a \emph{fake proof}\index{proof!fake}
1.503 pretending to solve the pending claim without further ado. This
1.504 only works in interactive development, or if the \verb|quick_and_dirty| flag is enabled (in ML). Facts emerging from fake
1.505 proofs are not the real thing. Internally, each theorem container
1.506 - is tainted by an oracle invocation, which is indicated as ``\isa{{\isachardoublequote}{\isacharbrackleft}{\isacharbang}{\isacharbrackright}{\isachardoublequote}}'' in the printed result.
1.507 + is tainted by an oracle invocation, which is indicated as ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{21}{\isacharbang}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}'' in the printed result.
1.508
1.509 The most important application of \hyperlink{command.sorry}{\mbox{\isa{\isacommand{sorry}}}} is to support
1.510 experimentation and top-down proof development.
1.511 @@ -708,7 +708,7 @@
1.512 \chref{ch:gen-tools} and \chref{ch:hol}).
1.513
1.514 \begin{matharray}{rcl}
1.515 - \indexdef{}{method}{-}\hypertarget{method.-}{\hyperlink{method.-}{\mbox{\isa{{\isacharminus}}}}} & : & \isa{method} \\
1.516 + \indexdef{}{method}{-}\hypertarget{method.-}{\hyperlink{method.-}{\mbox{\isa{{\isaliteral{2D}{\isacharminus}}}}}} & : & \isa{method} \\
1.517 \indexdef{}{method}{fact}\hypertarget{method.fact}{\hyperlink{method.fact}{\mbox{\isa{fact}}}} & : & \isa{method} \\
1.518 \indexdef{}{method}{assumption}\hypertarget{method.assumption}{\hyperlink{method.assumption}{\mbox{\isa{assumption}}}} & : & \isa{method} \\
1.519 \indexdef{}{method}{this}\hypertarget{method.this}{\hyperlink{method.this}{\mbox{\isa{this}}}} & : & \isa{method} \\
1.520 @@ -743,19 +743,19 @@
1.521
1.522 \begin{description}
1.523
1.524 - \item ``\hyperlink{method.-}{\mbox{\isa{{\isacharminus}}}}'' (minus) does nothing but insert the forward
1.525 + \item ``\hyperlink{method.-}{\mbox{\isa{{\isaliteral{2D}{\isacharminus}}}}}'' (minus) does nothing but insert the forward
1.526 chaining facts as premises into the goal. Note that command
1.527 \indexref{}{command}{proof}\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}} without any method actually performs a single
1.528 reduction step using the \indexref{}{method}{rule}\hyperlink{method.rule}{\mbox{\isa{rule}}} method; thus a plain
1.529 - \emph{do-nothing} proof step would be ``\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' rather than \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}} alone.
1.530 + \emph{do-nothing} proof step would be ``\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{22}{\isachardoublequote}}}'' rather than \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}} alone.
1.531
1.532 - \item \hyperlink{method.fact}{\mbox{\isa{fact}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} composes some fact from
1.533 - \isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ a\isactrlsub n{\isachardoublequote}} (or implicitly from the current proof context)
1.534 + \item \hyperlink{method.fact}{\mbox{\isa{fact}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} composes some fact from
1.535 + \isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} (or implicitly from the current proof context)
1.536 modulo unification of schematic type and term variables. The rule
1.537 structure is not taken into account, i.e.\ meta-level implication is
1.538 considered atomic. This is the same principle underlying literal
1.539 - facts (cf.\ \secref{sec:syn-att}): ``\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isachardoublequote}{\isasymphi}{\isachardoublequote}}~\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{fact}'' is equivalent to ``\hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\verb|`|\isa{{\isasymphi}}\verb|`|'' provided that
1.540 - \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymphi}{\isachardoublequote}} is an instance of some known \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymphi}{\isachardoublequote}} in the
1.541 + facts (cf.\ \secref{sec:syn-att}): ``\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{fact}'' is equivalent to ``\hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\verb|`|\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}}\verb|`|'' provided that
1.542 + \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} is an instance of some known \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} in the
1.543 proof context.
1.544
1.545 \item \hyperlink{method.assumption}{\mbox{\isa{assumption}}} solves some goal by a single assumption
1.546 @@ -767,9 +767,9 @@
1.547 all.
1.548
1.549 \item \hyperlink{method.this}{\mbox{\isa{this}}} applies all of the current facts directly as
1.550 - rules. Recall that ``\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isachardot}}}}}'' (dot) abbreviates ``\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{this}''.
1.551 + rules. Recall that ``\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}}}}}'' (dot) abbreviates ``\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{this}''.
1.552
1.553 - \item \hyperlink{method.rule}{\mbox{\isa{rule}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} applies some rule given as
1.554 + \item \hyperlink{method.rule}{\mbox{\isa{rule}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} applies some rule given as
1.555 argument in backward manner; facts are used to reduce the rule
1.556 before applying it to the goal. Thus \hyperlink{method.rule}{\mbox{\isa{rule}}} without facts
1.557 is plain introduction, while with facts it becomes elimination.
1.558 @@ -778,39 +778,39 @@
1.559 appropriate rules automatically, as declared in the current context
1.560 using the \hyperlink{attribute.Pure.intro}{\mbox{\isa{intro}}}, \hyperlink{attribute.Pure.elim}{\mbox{\isa{elim}}},
1.561 \hyperlink{attribute.Pure.dest}{\mbox{\isa{dest}}} attributes (see below). This is the
1.562 - default behavior of \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}} and ``\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}}''
1.563 + default behavior of \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}} and ``\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}}}}''
1.564 (double-dot) steps (see \secref{sec:proof-steps}).
1.565
1.566 \item \hyperlink{attribute.Pure.intro}{\mbox{\isa{intro}}}, \hyperlink{attribute.Pure.elim}{\mbox{\isa{elim}}}, and
1.567 \hyperlink{attribute.Pure.dest}{\mbox{\isa{dest}}} declare introduction, elimination, and
1.568 destruct rules, to be used with method \hyperlink{method.rule}{\mbox{\isa{rule}}}, and similar
1.569 tools. Note that the latter will ignore rules declared with
1.570 - ``\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}'', while ``\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}}'' are used most aggressively.
1.571 + ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}'', while ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}}'' are used most aggressively.
1.572
1.573 The classical reasoner (see \secref{sec:classical}) introduces its
1.574 own variants of these attributes; use qualified names to access the
1.575 - present versions of Isabelle/Pure, i.e.\ \hyperlink{attribute.Pure.Pure.intro}{\mbox{\isa{Pure{\isachardot}intro}}}.
1.576 + present versions of Isabelle/Pure, i.e.\ \hyperlink{attribute.Pure.Pure.intro}{\mbox{\isa{Pure{\isaliteral{2E}{\isachardot}}intro}}}.
1.577
1.578 \item \hyperlink{attribute.rule}{\mbox{\isa{rule}}}~\isa{del} undeclares introduction,
1.579 elimination, or destruct rules.
1.580
1.581 - \item \hyperlink{attribute.OF}{\mbox{\isa{OF}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} applies some
1.582 - theorem to all of the given rules \isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ a\isactrlsub n{\isachardoublequote}}
1.583 + \item \hyperlink{attribute.OF}{\mbox{\isa{OF}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} applies some
1.584 + theorem to all of the given rules \isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}
1.585 (in parallel). This corresponds to the \verb|op MRS| operation in
1.586 ML, but note the reversed order. Positions may be effectively
1.587 - skipped by including ``\isa{{\isacharunderscore}}'' (underscore) as argument.
1.588 + skipped by including ``\isa{{\isaliteral{5F}{\isacharunderscore}}}'' (underscore) as argument.
1.589
1.590 - \item \hyperlink{attribute.of}{\mbox{\isa{of}}}~\isa{{\isachardoublequote}t\isactrlsub {\isadigit{1}}\ {\isasymdots}\ t\isactrlsub n{\isachardoublequote}} performs positional
1.591 - instantiation of term variables. The terms \isa{{\isachardoublequote}t\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ t\isactrlsub n{\isachardoublequote}} are
1.592 + \item \hyperlink{attribute.of}{\mbox{\isa{of}}}~\isa{{\isaliteral{22}{\isachardoublequote}}t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} performs positional
1.593 + instantiation of term variables. The terms \isa{{\isaliteral{22}{\isachardoublequote}}t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} are
1.594 substituted for any schematic variables occurring in a theorem from
1.595 - left to right; ``\isa{{\isacharunderscore}}'' (underscore) indicates to skip a
1.596 - position. Arguments following a ``\isa{{\isachardoublequote}concl{\isacharcolon}{\isachardoublequote}}'' specification
1.597 + left to right; ``\isa{{\isaliteral{5F}{\isacharunderscore}}}'' (underscore) indicates to skip a
1.598 + position. Arguments following a ``\isa{{\isaliteral{22}{\isachardoublequote}}concl{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}}'' specification
1.599 refer to positions of the conclusion of a rule.
1.600
1.601 - \item \hyperlink{attribute.where}{\mbox{\isa{where}}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isacharequal}\ t\isactrlsub {\isadigit{1}}\ {\isasymAND}\ {\isasymdots}\ x\isactrlsub n\ {\isacharequal}\ t\isactrlsub n{\isachardoublequote}}
1.602 + \item \hyperlink{attribute.where}{\mbox{\isa{where}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3D}{\isacharequal}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}
1.603 performs named instantiation of schematic type and term variables
1.604 occurring in a theorem. Schematic variables have to be specified on
1.605 - the left-hand side (e.g.\ \isa{{\isachardoublequote}{\isacharquery}x{\isadigit{1}}{\isachardot}{\isadigit{3}}{\isachardoublequote}}). The question mark may
1.606 + the left-hand side (e.g.\ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}x{\isadigit{1}}{\isaliteral{2E}{\isachardot}}{\isadigit{3}}{\isaliteral{22}{\isachardoublequote}}}). The question mark may
1.607 be omitted if the variable name is a plain identifier without index.
1.608 As type instantiations are inferred from term instantiations,
1.609 explicit type instantiations are seldom necessary.
1.610 @@ -834,12 +834,12 @@
1.611 be used in scripts, too.
1.612
1.613 \begin{matharray}{rcl}
1.614 - \indexdef{}{command}{apply}\hypertarget{command.apply}{\hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
1.615 - \indexdef{}{command}{apply\_end}\hypertarget{command.apply-end}{\hyperlink{command.apply-end}{\mbox{\isa{\isacommand{apply{\isacharunderscore}end}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
1.616 - \indexdef{}{command}{done}\hypertarget{command.done}{\hyperlink{command.done}{\mbox{\isa{\isacommand{done}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ local{\isacharunderscore}theory\ {\isacharbar}\ theory{\isachardoublequote}} \\
1.617 - \indexdef{}{command}{defer}\hypertarget{command.defer}{\hyperlink{command.defer}{\mbox{\isa{\isacommand{defer}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}proof\ {\isasymrightarrow}\ proof{\isachardoublequote}} \\
1.618 - \indexdef{}{command}{prefer}\hypertarget{command.prefer}{\hyperlink{command.prefer}{\mbox{\isa{\isacommand{prefer}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}proof\ {\isasymrightarrow}\ proof{\isachardoublequote}} \\
1.619 - \indexdef{}{command}{back}\hypertarget{command.back}{\hyperlink{command.back}{\mbox{\isa{\isacommand{back}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}proof\ {\isasymrightarrow}\ proof{\isachardoublequote}} \\
1.620 + \indexdef{}{command}{apply}\hypertarget{command.apply}{\hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.621 + \indexdef{}{command}{apply\_end}\hypertarget{command.apply-end}{\hyperlink{command.apply-end}{\mbox{\isa{\isacommand{apply{\isaliteral{5F}{\isacharunderscore}}end}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.622 + \indexdef{}{command}{done}\hypertarget{command.done}{\hyperlink{command.done}{\mbox{\isa{\isacommand{done}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{7C}{\isacharbar}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
1.623 + \indexdef{}{command}{defer}\hypertarget{command.defer}{\hyperlink{command.defer}{\mbox{\isa{\isacommand{defer}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{22}{\isachardoublequote}}} \\
1.624 + \indexdef{}{command}{prefer}\hypertarget{command.prefer}{\hyperlink{command.prefer}{\mbox{\isa{\isacommand{prefer}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{22}{\isachardoublequote}}} \\
1.625 + \indexdef{}{command}{back}\hypertarget{command.back}{\hyperlink{command.back}{\mbox{\isa{\isacommand{back}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{22}{\isachardoublequote}}} \\
1.626 \end{matharray}
1.627
1.628 \begin{rail}
1.629 @@ -854,7 +854,7 @@
1.630 \begin{description}
1.631
1.632 \item \hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}~\isa{m} applies proof method \isa{m} in
1.633 - initial position, but unlike \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}} it retains ``\isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}}'' mode. Thus consecutive method applications may be
1.634 + initial position, but unlike \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}} it retains ``\isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' mode. Thus consecutive method applications may be
1.635 given just as in tactic scripts.
1.636
1.637 Facts are passed to \isa{m} as indicated by the goal's
1.638 @@ -862,7 +862,7 @@
1.639 further \hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}} command would always work in a purely
1.640 backward manner.
1.641
1.642 - \item \hyperlink{command.apply-end}{\mbox{\isa{\isacommand{apply{\isacharunderscore}end}}}}~\isa{{\isachardoublequote}m{\isachardoublequote}} applies proof method \isa{m} as if in terminal position. Basically, this simulates a
1.643 + \item \hyperlink{command.apply-end}{\mbox{\isa{\isacommand{apply{\isaliteral{5F}{\isacharunderscore}}end}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m{\isaliteral{22}{\isachardoublequote}}} applies proof method \isa{m} as if in terminal position. Basically, this simulates a
1.644 multi-step tactic script for \hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}, but may be given
1.645 anywhere within the proof body.
1.646
1.647 @@ -872,11 +872,11 @@
1.648
1.649 \item \hyperlink{command.done}{\mbox{\isa{\isacommand{done}}}} completes a proof script, provided that the
1.650 current goal state is solved completely. Note that actual
1.651 - structured proof commands (e.g.\ ``\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isachardot}}}}}'' or \hyperlink{command.sorry}{\mbox{\isa{\isacommand{sorry}}}}) may be used to conclude proof scripts as well.
1.652 + structured proof commands (e.g.\ ``\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}}}}}'' or \hyperlink{command.sorry}{\mbox{\isa{\isacommand{sorry}}}}) may be used to conclude proof scripts as well.
1.653
1.654 \item \hyperlink{command.defer}{\mbox{\isa{\isacommand{defer}}}}~\isa{n} and \hyperlink{command.prefer}{\mbox{\isa{\isacommand{prefer}}}}~\isa{n}
1.655 shuffle the list of pending goals: \hyperlink{command.defer}{\mbox{\isa{\isacommand{defer}}}} puts off
1.656 - sub-goal \isa{n} to the end of the list (\isa{{\isachardoublequote}n\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequote}} by
1.657 + sub-goal \isa{n} to the end of the list (\isa{{\isaliteral{22}{\isachardoublequote}}n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} by
1.658 default), while \hyperlink{command.prefer}{\mbox{\isa{\isacommand{prefer}}}} brings sub-goal \isa{n} to the
1.659 front.
1.660
1.661 @@ -899,7 +899,7 @@
1.662 %
1.663 \begin{isamarkuptext}%
1.664 \begin{matharray}{rcl}
1.665 - \indexdef{}{command}{method\_setup}\hypertarget{command.method-setup}{\hyperlink{command.method-setup}{\mbox{\isa{\isacommand{method{\isacharunderscore}setup}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
1.666 + \indexdef{}{command}{method\_setup}\hypertarget{command.method-setup}{\hyperlink{command.method-setup}{\mbox{\isa{\isacommand{method{\isaliteral{5F}{\isacharunderscore}}setup}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
1.667 \end{matharray}
1.668
1.669 \begin{rail}
1.670 @@ -909,8 +909,8 @@
1.671
1.672 \begin{description}
1.673
1.674 - \item \hyperlink{command.method-setup}{\mbox{\isa{\isacommand{method{\isacharunderscore}setup}}}}~\isa{{\isachardoublequote}name\ {\isacharequal}\ text\ description{\isachardoublequote}}
1.675 - defines a proof method in the current theory. The given \isa{{\isachardoublequote}text{\isachardoublequote}} has to be an ML expression of type
1.676 + \item \hyperlink{command.method-setup}{\mbox{\isa{\isacommand{method{\isaliteral{5F}{\isacharunderscore}}setup}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name\ {\isaliteral{3D}{\isacharequal}}\ text\ description{\isaliteral{22}{\isachardoublequote}}}
1.677 + defines a proof method in the current theory. The given \isa{{\isaliteral{22}{\isachardoublequote}}text{\isaliteral{22}{\isachardoublequote}}} has to be an ML expression of type
1.678 \verb|(Proof.context -> Proof.method) context_parser|, cf.\
1.679 basic parsers defined in structure \verb|Args| and \verb|Attrib|. There are also combinators like \verb|METHOD| and \verb|SIMPLE_METHOD| to turn certain tactic forms into official proof
1.680 methods; the primed versions refer to tactics with explicit goal
1.681 @@ -927,22 +927,22 @@
1.682 \endisadelimML
1.683 %
1.684 \isatagML
1.685 -\isacommand{method{\isacharunderscore}setup}\isamarkupfalse%
1.686 -\ my{\isacharunderscore}method{\isadigit{1}}\ {\isacharequal}\ {\isacharverbatimopen}\isanewline
1.687 -\ \ \ \ \ \ Scan{\isachardot}succeed\ {\isacharparenleft}K\ {\isacharparenleft}SIMPLE{\isacharunderscore}METHOD{\isacharprime}\ {\isacharparenleft}fn\ i{\isacharcolon}\ int\ {\isacharequal}{\isachargreater}\ no{\isacharunderscore}tac{\isacharparenright}{\isacharparenright}{\isacharparenright}\isanewline
1.688 -\ \ \ \ {\isacharverbatimclose}\ \ {\isachardoublequoteopen}my\ first\ method\ {\isacharparenleft}without\ any\ arguments{\isacharparenright}{\isachardoublequoteclose}\isanewline
1.689 +\isacommand{method{\isaliteral{5F}{\isacharunderscore}}setup}\isamarkupfalse%
1.690 +\ my{\isaliteral{5F}{\isacharunderscore}}method{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
1.691 +\ \ \ \ \ \ Scan{\isaliteral{2E}{\isachardot}}succeed\ {\isaliteral{28}{\isacharparenleft}}K\ {\isaliteral{28}{\isacharparenleft}}SIMPLE{\isaliteral{5F}{\isacharunderscore}}METHOD{\isaliteral{27}{\isacharprime}}\ {\isaliteral{28}{\isacharparenleft}}fn\ i{\isaliteral{3A}{\isacharcolon}}\ int\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ no{\isaliteral{5F}{\isacharunderscore}}tac{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
1.692 +\ \ \ \ {\isaliteral{2A7D}{\isacharverbatimclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}my\ first\ method\ {\isaliteral{28}{\isacharparenleft}}without\ any\ arguments{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
1.693 \isanewline
1.694 -\ \ \ \ \isacommand{method{\isacharunderscore}setup}\isamarkupfalse%
1.695 -\ my{\isacharunderscore}method{\isadigit{2}}\ {\isacharequal}\ {\isacharverbatimopen}\isanewline
1.696 -\ \ \ \ \ \ Scan{\isachardot}succeed\ {\isacharparenleft}fn\ ctxt{\isacharcolon}\ Proof{\isachardot}context\ {\isacharequal}{\isachargreater}\isanewline
1.697 -\ \ \ \ \ \ \ \ SIMPLE{\isacharunderscore}METHOD{\isacharprime}\ {\isacharparenleft}fn\ i{\isacharcolon}\ int\ {\isacharequal}{\isachargreater}\ no{\isacharunderscore}tac{\isacharparenright}{\isacharparenright}\isanewline
1.698 -\ \ \ \ {\isacharverbatimclose}\ \ {\isachardoublequoteopen}my\ second\ method\ {\isacharparenleft}with\ context{\isacharparenright}{\isachardoublequoteclose}\isanewline
1.699 +\ \ \ \ \isacommand{method{\isaliteral{5F}{\isacharunderscore}}setup}\isamarkupfalse%
1.700 +\ my{\isaliteral{5F}{\isacharunderscore}}method{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
1.701 +\ \ \ \ \ \ Scan{\isaliteral{2E}{\isachardot}}succeed\ {\isaliteral{28}{\isacharparenleft}}fn\ ctxt{\isaliteral{3A}{\isacharcolon}}\ Proof{\isaliteral{2E}{\isachardot}}context\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\isanewline
1.702 +\ \ \ \ \ \ \ \ SIMPLE{\isaliteral{5F}{\isacharunderscore}}METHOD{\isaliteral{27}{\isacharprime}}\ {\isaliteral{28}{\isacharparenleft}}fn\ i{\isaliteral{3A}{\isacharcolon}}\ int\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ no{\isaliteral{5F}{\isacharunderscore}}tac{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
1.703 +\ \ \ \ {\isaliteral{2A7D}{\isacharverbatimclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}my\ second\ method\ {\isaliteral{28}{\isacharparenleft}}with\ context{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
1.704 \isanewline
1.705 -\ \ \ \ \isacommand{method{\isacharunderscore}setup}\isamarkupfalse%
1.706 -\ my{\isacharunderscore}method{\isadigit{3}}\ {\isacharequal}\ {\isacharverbatimopen}\isanewline
1.707 -\ \ \ \ \ \ Attrib{\isachardot}thms\ {\isachargreater}{\isachargreater}\ {\isacharparenleft}fn\ thms{\isacharcolon}\ thm\ list\ {\isacharequal}{\isachargreater}\ fn\ ctxt{\isacharcolon}\ Proof{\isachardot}context\ {\isacharequal}{\isachargreater}\isanewline
1.708 -\ \ \ \ \ \ \ \ SIMPLE{\isacharunderscore}METHOD{\isacharprime}\ {\isacharparenleft}fn\ i{\isacharcolon}\ int\ {\isacharequal}{\isachargreater}\ no{\isacharunderscore}tac{\isacharparenright}{\isacharparenright}\isanewline
1.709 -\ \ \ \ {\isacharverbatimclose}\ \ {\isachardoublequoteopen}my\ third\ method\ {\isacharparenleft}with\ theorem\ arguments\ and\ context{\isacharparenright}{\isachardoublequoteclose}%
1.710 +\ \ \ \ \isacommand{method{\isaliteral{5F}{\isacharunderscore}}setup}\isamarkupfalse%
1.711 +\ my{\isaliteral{5F}{\isacharunderscore}}method{\isadigit{3}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
1.712 +\ \ \ \ \ \ Attrib{\isaliteral{2E}{\isachardot}}thms\ {\isaliteral{3E}{\isachargreater}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{28}{\isacharparenleft}}fn\ thms{\isaliteral{3A}{\isacharcolon}}\ thm\ list\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ fn\ ctxt{\isaliteral{3A}{\isacharcolon}}\ Proof{\isaliteral{2E}{\isachardot}}context\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\isanewline
1.713 +\ \ \ \ \ \ \ \ SIMPLE{\isaliteral{5F}{\isacharunderscore}}METHOD{\isaliteral{27}{\isacharprime}}\ {\isaliteral{28}{\isacharparenleft}}fn\ i{\isaliteral{3A}{\isacharcolon}}\ int\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ no{\isaliteral{5F}{\isacharunderscore}}tac{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
1.714 +\ \ \ \ {\isaliteral{2A7D}{\isacharverbatimclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}my\ third\ method\ {\isaliteral{28}{\isacharparenleft}}with\ theorem\ arguments\ and\ context{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
1.715 \endisatagML
1.716 {\isafoldML}%
1.717 %
1.718 @@ -956,8 +956,8 @@
1.719 %
1.720 \begin{isamarkuptext}%
1.721 \begin{matharray}{rcl}
1.722 - \indexdef{}{command}{obtain}\hypertarget{command.obtain}{\hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ proof{\isacharparenleft}chain{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
1.723 - \indexdef{}{command}{guess}\hypertarget{command.guess}{\hyperlink{command.guess}{\mbox{\isa{\isacommand{guess}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ proof{\isacharparenleft}chain{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
1.724 + \indexdef{}{command}{obtain}\hypertarget{command.obtain}{\hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.725 + \indexdef{}{command}{guess}\hypertarget{command.guess}{\hyperlink{command.guess}{\mbox{\isa{\isacommand{guess}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.726 \end{matharray}
1.727
1.728 Generalized elimination means that additional elements with certain
1.729 @@ -979,19 +979,19 @@
1.730 \end{rail}
1.731
1.732 The derived Isar command \hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}} is defined as follows
1.733 - (where \isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ b\isactrlsub k{\isachardoublequote}} shall refer to (optional)
1.734 + (where \isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub k{\isaliteral{22}{\isachardoublequote}}} shall refer to (optional)
1.735 facts indicated for forward chaining).
1.736 \begin{matharray}{l}
1.737 - \isa{{\isachardoublequote}{\isasymlangle}using\ b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub k{\isasymrangle}{\isachardoublequote}}~~\hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m\ {\isasymWHERE}\ a{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ \ {\isasymlangle}proof{\isasymrangle}\ {\isasymequiv}{\isachardoublequote}} \\[1ex]
1.738 - \quad \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isachardoublequote}{\isasymAnd}thesis{\isachardot}\ {\isacharparenleft}{\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardot}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ {\isasymLongrightarrow}\ thesis{\isacharparenright}\ {\isasymLongrightarrow}\ thesis{\isachardoublequote}} \\
1.739 + \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C616E676C653E}{\isasymlangle}}using\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub k{\isaliteral{5C3C72616E676C653E}{\isasymrangle}}{\isaliteral{22}{\isachardoublequote}}}~~\hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ \ {\isaliteral{5C3C6C616E676C653E}{\isasymlangle}}proof{\isaliteral{5C3C72616E676C653E}{\isasymrangle}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} \\[1ex]
1.740 + \quad \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}thesis{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ thesis{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ thesis{\isaliteral{22}{\isachardoublequote}}} \\
1.741 \quad \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\hyperlink{method.succeed}{\mbox{\isa{succeed}}} \\
1.742 \qquad \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{thesis} \\
1.743 - \qquad \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}that\ {\isacharbrackleft}Pure{\isachardot}intro{\isacharquery}{\isacharbrackright}{\isacharcolon}\ {\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardot}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ {\isasymLongrightarrow}\ thesis{\isachardoublequote}} \\
1.744 + \qquad \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}that\ {\isaliteral{5B}{\isacharbrackleft}}Pure{\isaliteral{2E}{\isachardot}}intro{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ thesis{\isaliteral{22}{\isachardoublequote}}} \\
1.745 \qquad \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}~\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{thesis} \\
1.746 - \quad\qquad \hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}~\isa{{\isacharminus}} \\
1.747 - \quad\qquad \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub k\ \ {\isasymlangle}proof{\isasymrangle}{\isachardoublequote}} \\
1.748 + \quad\qquad \hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}~\isa{{\isaliteral{2D}{\isacharminus}}} \\
1.749 + \quad\qquad \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub k\ \ {\isaliteral{5C3C6C616E676C653E}{\isasymlangle}}proof{\isaliteral{5C3C72616E676C653E}{\isasymrangle}}{\isaliteral{22}{\isachardoublequote}}} \\
1.750 \quad \hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}} \\
1.751 - \quad \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardoublequote}}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}\ a{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n{\isachardoublequote}} \\
1.752 + \quad \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}\ a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} \\
1.753 \end{matharray}
1.754
1.755 Typically, the soundness proof is relatively straight-forward, often
1.756 @@ -1015,9 +1015,9 @@
1.757 \medskip The improper variant \hyperlink{command.guess}{\mbox{\isa{\isacommand{guess}}}} is similar to
1.758 \hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}, but derives the obtained statement from the
1.759 course of reasoning! The proof starts with a fixed goal \isa{thesis}. The subsequent proof may refine this to anything of the
1.760 - form like \isa{{\isachardoublequote}{\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardot}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ {\isasymLongrightarrow}\ thesis{\isachardoublequote}}, but must not introduce new subgoals. The
1.761 + form like \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ thesis{\isaliteral{22}{\isachardoublequote}}}, but must not introduce new subgoals. The
1.762 final goal state is then used as reduction rule for the obtain
1.763 - scheme described above. Obtained parameters \isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m{\isachardoublequote}} are marked as internal by default, which prevents the
1.764 + scheme described above. Obtained parameters \isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}} are marked as internal by default, which prevents the
1.765 proof context from being polluted by ad-hoc variables. The variable
1.766 names and type constraints given as arguments for \hyperlink{command.guess}{\mbox{\isa{\isacommand{guess}}}}
1.767 specify a prefix of obtained parameters explicitly in the text.
1.768 @@ -1033,19 +1033,19 @@
1.769 %
1.770 \begin{isamarkuptext}%
1.771 \begin{matharray}{rcl}
1.772 - \indexdef{}{command}{also}\hypertarget{command.also}{\hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
1.773 - \indexdef{}{command}{finally}\hypertarget{command.finally}{\hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} \\
1.774 - \indexdef{}{command}{moreover}\hypertarget{command.moreover}{\hyperlink{command.moreover}{\mbox{\isa{\isacommand{moreover}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
1.775 - \indexdef{}{command}{ultimately}\hypertarget{command.ultimately}{\hyperlink{command.ultimately}{\mbox{\isa{\isacommand{ultimately}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} \\
1.776 - \indexdef{}{command}{print\_trans\_rules}\hypertarget{command.print-trans-rules}{\hyperlink{command.print-trans-rules}{\mbox{\isa{\isacommand{print{\isacharunderscore}trans{\isacharunderscore}rules}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
1.777 + \indexdef{}{command}{also}\hypertarget{command.also}{\hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.778 + \indexdef{}{command}{finally}\hypertarget{command.finally}{\hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.779 + \indexdef{}{command}{moreover}\hypertarget{command.moreover}{\hyperlink{command.moreover}{\mbox{\isa{\isacommand{moreover}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.780 + \indexdef{}{command}{ultimately}\hypertarget{command.ultimately}{\hyperlink{command.ultimately}{\mbox{\isa{\isacommand{ultimately}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.781 + \indexdef{}{command}{print\_trans\_rules}\hypertarget{command.print-trans-rules}{\hyperlink{command.print-trans-rules}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}trans{\isaliteral{5F}{\isacharunderscore}}rules}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
1.782 \hyperlink{attribute.trans}{\mbox{\isa{trans}}} & : & \isa{attribute} \\
1.783 \hyperlink{attribute.sym}{\mbox{\isa{sym}}} & : & \isa{attribute} \\
1.784 \hyperlink{attribute.symmetric}{\mbox{\isa{symmetric}}} & : & \isa{attribute} \\
1.785 \end{matharray}
1.786
1.787 Calculational proof is forward reasoning with implicit application
1.788 - of transitivity rules (such those of \isa{{\isachardoublequote}{\isacharequal}{\isachardoublequote}}, \isa{{\isachardoublequote}{\isasymle}{\isachardoublequote}},
1.789 - \isa{{\isachardoublequote}{\isacharless}{\isachardoublequote}}). Isabelle/Isar maintains an auxiliary fact register
1.790 + of transitivity rules (such those of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C653E}{\isasymle}}{\isaliteral{22}{\isachardoublequote}}},
1.791 + \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3C}{\isacharless}}{\isaliteral{22}{\isachardoublequote}}}). Isabelle/Isar maintains an auxiliary fact register
1.792 \indexref{}{fact}{calculation}\hyperlink{fact.calculation}{\mbox{\isa{calculation}}} for accumulating results obtained by
1.793 transitivity composed with the current result. Command \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}} updates \hyperlink{fact.calculation}{\mbox{\isa{calculation}}} involving \hyperlink{fact.this}{\mbox{\isa{this}}}, while
1.794 \hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}} exhibits the final \hyperlink{fact.calculation}{\mbox{\isa{calculation}}} by
1.795 @@ -1056,7 +1056,7 @@
1.796 but only collect further results in \hyperlink{fact.calculation}{\mbox{\isa{calculation}}} without
1.797 applying any rules yet.
1.798
1.799 - Also note that the implicit term abbreviation ``\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}'' has
1.800 + Also note that the implicit term abbreviation ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}'' has
1.801 its canonical application with calculational proofs. It refers to
1.802 the argument of the preceding statement. (The argument of a curried
1.803 infix expression happens to be its right-hand side.)
1.804 @@ -1073,10 +1073,10 @@
1.805 handling of block-structure.}
1.806
1.807 \begin{matharray}{rcl}
1.808 - \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}\isa{{\isachardoublequote}\isactrlsub {\isadigit{0}}{\isachardoublequote}} & \equiv & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isachardoublequote}calculation\ {\isacharequal}\ this{\isachardoublequote}} \\
1.809 - \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}\isa{{\isachardoublequote}\isactrlsub n{\isacharplus}{\isadigit{1}}{\isachardoublequote}} & \equiv & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isachardoublequote}calculation\ {\isacharequal}\ trans\ {\isacharbrackleft}OF\ calculation\ this{\isacharbrackright}{\isachardoublequote}} \\[0.5ex]
1.810 + \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{0}}{\isaliteral{22}{\isachardoublequote}}} & \equiv & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}calculation\ {\isaliteral{3D}{\isacharequal}}\ this{\isaliteral{22}{\isachardoublequote}}} \\
1.811 + \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{2B}{\isacharplus}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & \equiv & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}calculation\ {\isaliteral{3D}{\isacharequal}}\ trans\ {\isaliteral{5B}{\isacharbrackleft}}OF\ calculation\ this{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} \\[0.5ex]
1.812 \hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}} & \equiv & \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}~\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{calculation} \\[0.5ex]
1.813 - \hyperlink{command.moreover}{\mbox{\isa{\isacommand{moreover}}}} & \equiv & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isachardoublequote}calculation\ {\isacharequal}\ calculation\ this{\isachardoublequote}} \\
1.814 + \hyperlink{command.moreover}{\mbox{\isa{\isacommand{moreover}}}} & \equiv & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}calculation\ {\isaliteral{3D}{\isacharequal}}\ calculation\ this{\isaliteral{22}{\isachardoublequote}}} \\
1.815 \hyperlink{command.ultimately}{\mbox{\isa{\isacommand{ultimately}}}} & \equiv & \hyperlink{command.moreover}{\mbox{\isa{\isacommand{moreover}}}}~\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{calculation} \\
1.816 \end{matharray}
1.817
1.818 @@ -1089,7 +1089,7 @@
1.819
1.820 \begin{description}
1.821
1.822 - \item \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}~\isa{{\isachardoublequote}{\isacharparenleft}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharparenright}{\isachardoublequote}} maintains the auxiliary
1.823 + \item \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} maintains the auxiliary
1.824 \hyperlink{fact.calculation}{\mbox{\isa{calculation}}} register as follows. The first occurrence of
1.825 \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}} in some calculational thread initializes \hyperlink{fact.calculation}{\mbox{\isa{calculation}}} by \hyperlink{fact.this}{\mbox{\isa{this}}}. Any subsequent \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}} on
1.826 the same level of block-structure updates \hyperlink{fact.calculation}{\mbox{\isa{calculation}}} by
1.827 @@ -1097,16 +1097,16 @@
1.828 current context, unless alternative rules are given as explicit
1.829 arguments.
1.830
1.831 - \item \hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}~\isa{{\isachardoublequote}{\isacharparenleft}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharparenright}{\isachardoublequote}} maintaining \hyperlink{fact.calculation}{\mbox{\isa{calculation}}} in the same way as \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}, and concludes the
1.832 + \item \hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} maintaining \hyperlink{fact.calculation}{\mbox{\isa{calculation}}} in the same way as \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}, and concludes the
1.833 current calculational thread. The final result is exhibited as fact
1.834 for forward chaining towards the next goal. Basically, \hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}} just abbreviates \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}~\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\hyperlink{fact.calculation}{\mbox{\isa{calculation}}}. Typical idioms for concluding
1.835 - calculational proofs are ``\hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}~\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{{\isacharquery}thesis}~\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isachardot}}}}}'' and ``\hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}~\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isasymphi}}~\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isachardot}}}}}''.
1.836 + calculational proofs are ``\hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}~\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{{\isaliteral{3F}{\isacharquery}}thesis}~\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}}}}}'' and ``\hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}~\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}}~\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}}}}}''.
1.837
1.838 \item \hyperlink{command.moreover}{\mbox{\isa{\isacommand{moreover}}}} and \hyperlink{command.ultimately}{\mbox{\isa{\isacommand{ultimately}}}} are
1.839 analogous to \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}} and \hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}, but collect
1.840 results only, without applying rules.
1.841
1.842 - \item \hyperlink{command.print-trans-rules}{\mbox{\isa{\isacommand{print{\isacharunderscore}trans{\isacharunderscore}rules}}}} prints the list of transitivity
1.843 + \item \hyperlink{command.print-trans-rules}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}trans{\isaliteral{5F}{\isacharunderscore}}rules}}}} prints the list of transitivity
1.844 rules (for calculational commands \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}} and \hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}) and symmetry rules (for the \hyperlink{attribute.symmetric}{\mbox{\isa{symmetric}}}
1.845 operation and single step elimination patters) of the current
1.846 context.
1.847 @@ -1114,15 +1114,15 @@
1.848 \item \hyperlink{attribute.trans}{\mbox{\isa{trans}}} declares theorems as transitivity rules.
1.849
1.850 \item \hyperlink{attribute.sym}{\mbox{\isa{sym}}} declares symmetry rules, as well as
1.851 - \hyperlink{attribute.Pure.elim}{\mbox{\isa{Pure{\isachardot}elim}}}\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}} rules.
1.852 + \hyperlink{attribute.Pure.elim}{\mbox{\isa{Pure{\isaliteral{2E}{\isachardot}}elim}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}} rules.
1.853
1.854 \item \hyperlink{attribute.symmetric}{\mbox{\isa{symmetric}}} resolves a theorem with some rule
1.855 declared as \hyperlink{attribute.sym}{\mbox{\isa{sym}}} in the current context. For example,
1.856 - ``\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}{\isacharbrackleft}symmetric{\isacharbrackright}{\isacharcolon}\ x\ {\isacharequal}\ y{\isachardoublequote}}'' produces a
1.857 + ``\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}symmetric{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequote}}}'' produces a
1.858 swapped fact derived from that assumption.
1.859
1.860 In structured proof texts it is often more appropriate to use an
1.861 - explicit single-step elimination proof, such as ``\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}x\ {\isacharequal}\ y{\isachardoublequote}}~\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}~\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isachardoublequote}y\ {\isacharequal}\ x{\isachardoublequote}}~\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}}''.
1.862 + explicit single-step elimination proof, such as ``\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}~\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}y\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}}}}''.
1.863
1.864 \end{description}%
1.865 \end{isamarkuptext}%
1.866 @@ -1138,10 +1138,10 @@
1.867 %
1.868 \begin{isamarkuptext}%
1.869 \begin{matharray}{rcl}
1.870 - \indexdef{}{command}{case}\hypertarget{command.case}{\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
1.871 - \indexdef{}{command}{print\_cases}\hypertarget{command.print-cases}{\hyperlink{command.print-cases}{\mbox{\isa{\isacommand{print{\isacharunderscore}cases}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
1.872 - \indexdef{}{attribute}{case\_names}\hypertarget{attribute.case-names}{\hyperlink{attribute.case-names}{\mbox{\isa{case{\isacharunderscore}names}}}} & : & \isa{attribute} \\
1.873 - \indexdef{}{attribute}{case\_conclusion}\hypertarget{attribute.case-conclusion}{\hyperlink{attribute.case-conclusion}{\mbox{\isa{case{\isacharunderscore}conclusion}}}} & : & \isa{attribute} \\
1.874 + \indexdef{}{command}{case}\hypertarget{command.case}{\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
1.875 + \indexdef{}{command}{print\_cases}\hypertarget{command.print-cases}{\hyperlink{command.print-cases}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}cases}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
1.876 + \indexdef{}{attribute}{case\_names}\hypertarget{attribute.case-names}{\hyperlink{attribute.case-names}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}names}}}} & : & \isa{attribute} \\
1.877 + \indexdef{}{attribute}{case\_conclusion}\hypertarget{attribute.case-conclusion}{\hyperlink{attribute.case-conclusion}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}conclusion}}}} & : & \isa{attribute} \\
1.878 \indexdef{}{attribute}{params}\hypertarget{attribute.params}{\hyperlink{attribute.params}{\mbox{\isa{params}}}} & : & \isa{attribute} \\
1.879 \indexdef{}{attribute}{consumes}\hypertarget{attribute.consumes}{\hyperlink{attribute.consumes}{\mbox{\isa{consumes}}}} & : & \isa{attribute} \\
1.880 \end{matharray}
1.881 @@ -1155,20 +1155,20 @@
1.882
1.883 The \hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}} command provides a shorthand to refer to a
1.884 local context symbolically: certain proof methods provide an
1.885 - environment of named ``cases'' of the form \isa{{\isachardoublequote}c{\isacharcolon}\ x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m{\isacharcomma}\ {\isasymphi}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymphi}\isactrlsub n{\isachardoublequote}}; the effect of ``\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{c}'' is then equivalent to ``\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardoublequote}}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}c{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n{\isachardoublequote}}''. Term bindings may be covered as well, notably
1.886 - \hyperlink{variable.?case}{\mbox{\isa{{\isacharquery}case}}} for the main conclusion.
1.887 + environment of named ``cases'' of the form \isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{3A}{\isacharcolon}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}; the effect of ``\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{c}'' is then equivalent to ``\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}''. Term bindings may be covered as well, notably
1.888 + \hyperlink{variable.?case}{\mbox{\isa{{\isaliteral{3F}{\isacharquery}}case}}} for the main conclusion.
1.889
1.890 - By default, the ``terminology'' \isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m{\isachardoublequote}} of
1.891 + By default, the ``terminology'' \isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}} of
1.892 a case value is marked as hidden, i.e.\ there is no way to refer to
1.893 such parameters in the subsequent proof text. After all, original
1.894 rule parameters stem from somewhere outside of the current proof
1.895 - text. By using the explicit form ``\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{{\isachardoublequote}{\isacharparenleft}c\ y\isactrlsub {\isadigit{1}}\ {\isasymdots}\ y\isactrlsub m{\isacharparenright}{\isachardoublequote}}'' instead, the proof author is able to
1.896 + text. By using the explicit form ``\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}c\ y\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ y\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' instead, the proof author is able to
1.897 chose local names that fit nicely into the current context.
1.898
1.899 \medskip It is important to note that proper use of \hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}} does not provide means to peek at the current goal state,
1.900 which is not directly observable in Isar! Nonetheless, goal
1.901 - refinement commands do provide named cases \isa{{\isachardoublequote}goal\isactrlsub i{\isachardoublequote}}
1.902 - for each subgoal \isa{{\isachardoublequote}i\ {\isacharequal}\ {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ n{\isachardoublequote}} of the resulting goal state.
1.903 + refinement commands do provide named cases \isa{{\isaliteral{22}{\isachardoublequote}}goal\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}}
1.904 + for each subgoal \isa{{\isaliteral{22}{\isachardoublequote}}i\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ n{\isaliteral{22}{\isachardoublequote}}} of the resulting goal state.
1.905 Using this extra feature requires great care, because some bits of
1.906 the internal tactical machinery intrude the proof text. In
1.907 particular, parameter names stemming from the left-over of automated
1.908 @@ -1204,28 +1204,28 @@
1.909
1.910 \begin{description}
1.911
1.912 - \item \hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{{\isachardoublequote}{\isacharparenleft}c\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isacharparenright}{\isachardoublequote}} invokes a named local
1.913 - context \isa{{\isachardoublequote}c{\isacharcolon}\ x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m{\isacharcomma}\ {\isasymphi}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymphi}\isactrlsub m{\isachardoublequote}}, as provided by an
1.914 + \item \hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}c\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} invokes a named local
1.915 + context \isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{3A}{\isacharcolon}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}}, as provided by an
1.916 appropriate proof method (such as \indexref{}{method}{cases}\hyperlink{method.cases}{\mbox{\isa{cases}}} and
1.917 - \indexref{}{method}{induct}\hyperlink{method.induct}{\mbox{\isa{induct}}}). The command ``\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{{\isachardoublequote}{\isacharparenleft}c\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isacharparenright}{\isachardoublequote}}'' abbreviates ``\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardoublequote}}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}c{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n{\isachardoublequote}}''.
1.918 + \indexref{}{method}{induct}\hyperlink{method.induct}{\mbox{\isa{induct}}}). The command ``\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}c\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' abbreviates ``\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}''.
1.919
1.920 - \item \hyperlink{command.print-cases}{\mbox{\isa{\isacommand{print{\isacharunderscore}cases}}}} prints all local contexts of the
1.921 + \item \hyperlink{command.print-cases}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}cases}}}} prints all local contexts of the
1.922 current state, using Isar proof language notation.
1.923
1.924 - \item \hyperlink{attribute.case-names}{\mbox{\isa{case{\isacharunderscore}names}}}~\isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}\ {\isasymdots}\ c\isactrlsub k{\isachardoublequote}} declares names for
1.925 - the local contexts of premises of a theorem; \isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub k{\isachardoublequote}}
1.926 + \item \hyperlink{attribute.case-names}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}names}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub k{\isaliteral{22}{\isachardoublequote}}} declares names for
1.927 + the local contexts of premises of a theorem; \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub k{\isaliteral{22}{\isachardoublequote}}}
1.928 refers to the \emph{suffix} of the list of premises.
1.929
1.930 - \item \hyperlink{attribute.case-conclusion}{\mbox{\isa{case{\isacharunderscore}conclusion}}}~\isa{{\isachardoublequote}c\ d\isactrlsub {\isadigit{1}}\ {\isasymdots}\ d\isactrlsub k{\isachardoublequote}} declares
1.931 - names for the conclusions of a named premise \isa{c}; here \isa{{\isachardoublequote}d\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ d\isactrlsub k{\isachardoublequote}} refers to the prefix of arguments of a logical formula
1.932 - built by nesting a binary connective (e.g.\ \isa{{\isachardoublequote}{\isasymor}{\isachardoublequote}}).
1.933 + \item \hyperlink{attribute.case-conclusion}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}conclusion}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ d\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ d\isaliteral{5C3C5E7375623E}{}\isactrlsub k{\isaliteral{22}{\isachardoublequote}}} declares
1.934 + names for the conclusions of a named premise \isa{c}; here \isa{{\isaliteral{22}{\isachardoublequote}}d\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ d\isaliteral{5C3C5E7375623E}{}\isactrlsub k{\isaliteral{22}{\isachardoublequote}}} refers to the prefix of arguments of a logical formula
1.935 + built by nesting a binary connective (e.g.\ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6F723E}{\isasymor}}{\isaliteral{22}{\isachardoublequote}}}).
1.936
1.937 Note that proof methods such as \hyperlink{method.induct}{\mbox{\isa{induct}}} and \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}} already provide a default name for the conclusion as a
1.938 whole. The need to name subformulas only arises with cases that
1.939 split into several sub-cases, as in common co-induction rules.
1.940
1.941 - \item \hyperlink{attribute.params}{\mbox{\isa{params}}}~\isa{{\isachardoublequote}p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub m\ {\isasymAND}\ {\isasymdots}\ q\isactrlsub {\isadigit{1}}\ {\isasymdots}\ q\isactrlsub n{\isachardoublequote}} renames
1.942 - the innermost parameters of premises \isa{{\isachardoublequote}{\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ n{\isachardoublequote}} of some
1.943 + \item \hyperlink{attribute.params}{\mbox{\isa{params}}}~\isa{{\isaliteral{22}{\isachardoublequote}}p\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub m\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ q\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ q\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} renames
1.944 + the innermost parameters of premises \isa{{\isaliteral{22}{\isachardoublequote}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ n{\isaliteral{22}{\isachardoublequote}}} of some
1.945 theorem. An empty list of names may be given to skip positions,
1.946 leaving the present parameters unchanged.
1.947
1.948 @@ -1235,7 +1235,7 @@
1.949 \item \hyperlink{attribute.consumes}{\mbox{\isa{consumes}}}~\isa{n} declares the number of ``major
1.950 premises'' of a rule, i.e.\ the number of facts to be consumed when
1.951 it is applied by an appropriate proof method. The default value of
1.952 - \hyperlink{attribute.consumes}{\mbox{\isa{consumes}}} is \isa{{\isachardoublequote}n\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequote}}, which is appropriate for
1.953 + \hyperlink{attribute.consumes}{\mbox{\isa{consumes}}} is \isa{{\isaliteral{22}{\isachardoublequote}}n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}, which is appropriate for
1.954 the usual kind of cases and induction rules for inductive sets (cf.\
1.955 \secref{sec:hol-inductive}). Rules without any \hyperlink{attribute.consumes}{\mbox{\isa{consumes}}} declaration given are treated as if \hyperlink{attribute.consumes}{\mbox{\isa{consumes}}}~\isa{{\isadigit{0}}} had been specified.
1.956
1.957 @@ -1296,7 +1296,7 @@
1.958
1.959 \begin{description}
1.960
1.961 - \item \hyperlink{method.cases}{\mbox{\isa{cases}}}~\isa{{\isachardoublequote}insts\ R{\isachardoublequote}} applies method \hyperlink{method.rule}{\mbox{\isa{rule}}} with an appropriate case distinction theorem, instantiated to
1.962 + \item \hyperlink{method.cases}{\mbox{\isa{cases}}}~\isa{{\isaliteral{22}{\isachardoublequote}}insts\ R{\isaliteral{22}{\isachardoublequote}}} applies method \hyperlink{method.rule}{\mbox{\isa{rule}}} with an appropriate case distinction theorem, instantiated to
1.963 the subjects \isa{insts}. Symbolic case names are bound according
1.964 to the rule's local contexts.
1.965
1.966 @@ -1308,8 +1308,8 @@
1.967 facts & & arguments & rule \\\hline
1.968 & \hyperlink{method.cases}{\mbox{\isa{cases}}} & & classical case split \\
1.969 & \hyperlink{method.cases}{\mbox{\isa{cases}}} & \isa{t} & datatype exhaustion (type of \isa{t}) \\
1.970 - \isa{{\isachardoublequote}{\isasymturnstile}\ A\ t{\isachardoublequote}} & \hyperlink{method.cases}{\mbox{\isa{cases}}} & \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} & inductive predicate/set elimination (of \isa{A}) \\
1.971 - \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} & \hyperlink{method.cases}{\mbox{\isa{cases}}} & \isa{{\isachardoublequote}{\isasymdots}\ rule{\isacharcolon}\ R{\isachardoublequote}} & explicit rule \isa{R} \\
1.972 + \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A\ t{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{method.cases}{\mbox{\isa{cases}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} & inductive predicate/set elimination (of \isa{A}) \\
1.973 + \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{method.cases}{\mbox{\isa{cases}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ rule{\isaliteral{3A}{\isacharcolon}}\ R{\isaliteral{22}{\isachardoublequote}}} & explicit rule \isa{R} \\
1.974 \end{tabular}
1.975 \medskip
1.976
1.977 @@ -1317,31 +1317,31 @@
1.978 of premises of the case rule; within each premise, the \emph{prefix}
1.979 of variables is instantiated. In most situations, only a single
1.980 term needs to be specified; this refers to the first variable of the
1.981 - last premise (it is usually the same for all cases). The \isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}simp{\isacharparenright}{\isachardoublequote}} option can be used to disable pre-simplification of
1.982 + last premise (it is usually the same for all cases). The \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} option can be used to disable pre-simplification of
1.983 cases (see the description of \hyperlink{method.induct}{\mbox{\isa{induct}}} below for details).
1.984
1.985 - \item \hyperlink{method.induct}{\mbox{\isa{induct}}}~\isa{{\isachardoublequote}insts\ R{\isachardoublequote}} is analogous to the
1.986 + \item \hyperlink{method.induct}{\mbox{\isa{induct}}}~\isa{{\isaliteral{22}{\isachardoublequote}}insts\ R{\isaliteral{22}{\isachardoublequote}}} is analogous to the
1.987 \hyperlink{method.cases}{\mbox{\isa{cases}}} method, but refers to induction rules, which are
1.988 determined as follows:
1.989
1.990 \medskip
1.991 \begin{tabular}{llll}
1.992 facts & & arguments & rule \\\hline
1.993 - & \hyperlink{method.induct}{\mbox{\isa{induct}}} & \isa{{\isachardoublequote}P\ x{\isachardoublequote}} & datatype induction (type of \isa{x}) \\
1.994 - \isa{{\isachardoublequote}{\isasymturnstile}\ A\ x{\isachardoublequote}} & \hyperlink{method.induct}{\mbox{\isa{induct}}} & \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} & predicate/set induction (of \isa{A}) \\
1.995 - \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} & \hyperlink{method.induct}{\mbox{\isa{induct}}} & \isa{{\isachardoublequote}{\isasymdots}\ rule{\isacharcolon}\ R{\isachardoublequote}} & explicit rule \isa{R} \\
1.996 + & \hyperlink{method.induct}{\mbox{\isa{induct}}} & \isa{{\isaliteral{22}{\isachardoublequote}}P\ x{\isaliteral{22}{\isachardoublequote}}} & datatype induction (type of \isa{x}) \\
1.997 + \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A\ x{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{method.induct}{\mbox{\isa{induct}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} & predicate/set induction (of \isa{A}) \\
1.998 + \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{method.induct}{\mbox{\isa{induct}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ rule{\isaliteral{3A}{\isacharcolon}}\ R{\isaliteral{22}{\isachardoublequote}}} & explicit rule \isa{R} \\
1.999 \end{tabular}
1.1000 \medskip
1.1001
1.1002 Several instantiations may be given, each referring to some part of
1.1003 a mutual inductive definition or datatype --- only related partial
1.1004 induction rules may be used together, though. Any of the lists of
1.1005 - terms \isa{{\isachardoublequote}P{\isacharcomma}\ x{\isacharcomma}\ {\isasymdots}{\isachardoublequote}} refers to the \emph{suffix} of variables
1.1006 + terms \isa{{\isaliteral{22}{\isachardoublequote}}P{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} refers to the \emph{suffix} of variables
1.1007 present in the induction rule. This enables the writer to specify
1.1008 only induction variables, or both predicates and variables, for
1.1009 example.
1.1010
1.1011 - Instantiations may be definitional: equations \isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}}
1.1012 + Instantiations may be definitional: equations \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}}
1.1013 introduce local definitions, which are inserted into the claim and
1.1014 discharged after applying the induction rule. Equalities reappear
1.1015 in the inductive cases, but have been transformed according to the
1.1016 @@ -1349,7 +1349,7 @@
1.1017 practically useful induction hypotheses, some variables occurring in
1.1018 \isa{t} need to be fixed (see below). Instantiations of the form
1.1019 \isa{t}, where \isa{t} is not a variable, are taken as a
1.1020 - shorthand for \mbox{\isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}}}, where \isa{x} is a fresh
1.1021 + shorthand for \mbox{\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}}}, where \isa{x} is a fresh
1.1022 variable. If this is not intended, \isa{t} has to be enclosed in
1.1023 parentheses. By default, the equalities generated by definitional
1.1024 instantiations are pre-simplified using a specific set of rules,
1.1025 @@ -1357,23 +1357,23 @@
1.1026 datatypes. This pre-simplification may cause some of the parameters
1.1027 of an inductive case to disappear, or may even completely delete
1.1028 some of the inductive cases, if one of the equalities occurring in
1.1029 - their premises can be simplified to \isa{False}. The \isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}simp{\isacharparenright}{\isachardoublequote}} option can be used to disable pre-simplification.
1.1030 + their premises can be simplified to \isa{False}. The \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} option can be used to disable pre-simplification.
1.1031 Additional rules to be used in pre-simplification can be declared
1.1032 - using the \indexdef{}{attribute}{induct\_simp}\hypertarget{attribute.induct-simp}{\hyperlink{attribute.induct-simp}{\mbox{\isa{induct{\isacharunderscore}simp}}}} attribute.
1.1033 + using the \indexdef{}{attribute}{induct\_simp}\hypertarget{attribute.induct-simp}{\hyperlink{attribute.induct-simp}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}simp}}}} attribute.
1.1034
1.1035 - The optional ``\isa{{\isachardoublequote}arbitrary{\isacharcolon}\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardoublequote}}''
1.1036 - specification generalizes variables \isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m{\isachardoublequote}} of the original goal before applying induction. Thus
1.1037 + The optional ``\isa{{\isaliteral{22}{\isachardoublequote}}arbitrary{\isaliteral{3A}{\isacharcolon}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}}''
1.1038 + specification generalizes variables \isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}} of the original goal before applying induction. Thus
1.1039 induction hypotheses may become sufficiently general to get the
1.1040 proof through. Together with definitional instantiations, one may
1.1041 effectively perform induction over expressions of a certain
1.1042 structure.
1.1043
1.1044 - The optional ``\isa{{\isachardoublequote}taking{\isacharcolon}\ t\isactrlsub {\isadigit{1}}\ {\isasymdots}\ t\isactrlsub n{\isachardoublequote}}''
1.1045 + The optional ``\isa{{\isaliteral{22}{\isachardoublequote}}taking{\isaliteral{3A}{\isacharcolon}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}''
1.1046 specification provides additional instantiations of a prefix of
1.1047 pending variables in the rule. Such schematic induction rules
1.1048 rarely occur in practice, though.
1.1049
1.1050 - \item \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}}~\isa{{\isachardoublequote}inst\ R{\isachardoublequote}} is analogous to the
1.1051 + \item \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}}~\isa{{\isaliteral{22}{\isachardoublequote}}inst\ R{\isaliteral{22}{\isachardoublequote}}} is analogous to the
1.1052 \hyperlink{method.induct}{\mbox{\isa{induct}}} method, but refers to coinduction rules, which are
1.1053 determined as follows:
1.1054
1.1055 @@ -1381,20 +1381,20 @@
1.1056 \begin{tabular}{llll}
1.1057 goal & & arguments & rule \\\hline
1.1058 & \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}} & \isa{x} & type coinduction (type of \isa{x}) \\
1.1059 - \isa{{\isachardoublequote}A\ x{\isachardoublequote}} & \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}} & \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} & predicate/set coinduction (of \isa{A}) \\
1.1060 - \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} & \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}} & \isa{{\isachardoublequote}{\isasymdots}\ rule{\isacharcolon}\ R{\isachardoublequote}} & explicit rule \isa{R} \\
1.1061 + \isa{{\isaliteral{22}{\isachardoublequote}}A\ x{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} & predicate/set coinduction (of \isa{A}) \\
1.1062 + \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ rule{\isaliteral{3A}{\isacharcolon}}\ R{\isaliteral{22}{\isachardoublequote}}} & explicit rule \isa{R} \\
1.1063 \end{tabular}
1.1064
1.1065 Coinduction is the dual of induction. Induction essentially
1.1066 - eliminates \isa{{\isachardoublequote}A\ x{\isachardoublequote}} towards a generic result \isa{{\isachardoublequote}P\ x{\isachardoublequote}},
1.1067 - while coinduction introduces \isa{{\isachardoublequote}A\ x{\isachardoublequote}} starting with \isa{{\isachardoublequote}B\ x{\isachardoublequote}}, for a suitable ``bisimulation'' \isa{B}. The cases of a
1.1068 + eliminates \isa{{\isaliteral{22}{\isachardoublequote}}A\ x{\isaliteral{22}{\isachardoublequote}}} towards a generic result \isa{{\isaliteral{22}{\isachardoublequote}}P\ x{\isaliteral{22}{\isachardoublequote}}},
1.1069 + while coinduction introduces \isa{{\isaliteral{22}{\isachardoublequote}}A\ x{\isaliteral{22}{\isachardoublequote}}} starting with \isa{{\isaliteral{22}{\isachardoublequote}}B\ x{\isaliteral{22}{\isachardoublequote}}}, for a suitable ``bisimulation'' \isa{B}. The cases of a
1.1070 coinduct rule are typically named after the predicates or sets being
1.1071 covered, while the conclusions consist of several alternatives being
1.1072 named after the individual destructor patterns.
1.1073
1.1074 The given instantiation refers to the \emph{suffix} of variables
1.1075 occurring in the rule's major premise, or conclusion if unavailable.
1.1076 - An additional ``\isa{{\isachardoublequote}taking{\isacharcolon}\ t\isactrlsub {\isadigit{1}}\ {\isasymdots}\ t\isactrlsub n{\isachardoublequote}}''
1.1077 + An additional ``\isa{{\isaliteral{22}{\isachardoublequote}}taking{\isaliteral{3A}{\isacharcolon}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}''
1.1078 specification may be required in order to specify the bisimulation
1.1079 to be used in the coinduction step.
1.1080
1.1081 @@ -1404,17 +1404,17 @@
1.1082 instantiated rule as given in the text. Beyond that, the \hyperlink{method.induct}{\mbox{\isa{induct}}} and \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}} methods guess further instantiations
1.1083 from the goal specification itself. Any persisting unresolved
1.1084 schematic variables of the resulting rule will render the the
1.1085 - corresponding case invalid. The term binding \hyperlink{variable.?case}{\mbox{\isa{{\isacharquery}case}}} for
1.1086 + corresponding case invalid. The term binding \hyperlink{variable.?case}{\mbox{\isa{{\isaliteral{3F}{\isacharquery}}case}}} for
1.1087 the conclusion will be provided with each case, provided that term
1.1088 is fully specified.
1.1089
1.1090 - The \hyperlink{command.print-cases}{\mbox{\isa{\isacommand{print{\isacharunderscore}cases}}}} command prints all named cases present
1.1091 + The \hyperlink{command.print-cases}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}cases}}}} command prints all named cases present
1.1092 in the current proof state.
1.1093
1.1094 \medskip Despite the additional infrastructure, both \hyperlink{method.cases}{\mbox{\isa{cases}}}
1.1095 and \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}} merely apply a certain rule, after
1.1096 instantiation, while conforming due to the usual way of monotonic
1.1097 - natural deduction: the context of a structured statement \isa{{\isachardoublequote}{\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardot}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ {\isasymLongrightarrow}\ {\isasymdots}{\isachardoublequote}}
1.1098 + natural deduction: the context of a structured statement \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}
1.1099 reappears unchanged after the case split.
1.1100
1.1101 The \hyperlink{method.induct}{\mbox{\isa{induct}}} method is fundamentally different in this
1.1102 @@ -1429,7 +1429,7 @@
1.1103 In induction proofs, local assumptions introduced by cases are split
1.1104 into two different kinds: \isa{hyps} stemming from the rule and
1.1105 \isa{prems} from the goal statement. This is reflected in the
1.1106 - extracted cases accordingly, so invoking ``\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{c}'' will provide separate facts \isa{c{\isachardot}hyps} and \isa{c{\isachardot}prems},
1.1107 + extracted cases accordingly, so invoking ``\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{c}'' will provide separate facts \isa{c{\isaliteral{2E}{\isachardot}}hyps} and \isa{c{\isaliteral{2E}{\isachardot}}prems},
1.1108 as well as fact \isa{c} to hold the all-inclusive list.
1.1109
1.1110 \medskip Facts presented to either method are consumed according to
1.1111 @@ -1448,7 +1448,7 @@
1.1112 %
1.1113 \begin{isamarkuptext}%
1.1114 \begin{matharray}{rcl}
1.1115 - \indexdef{}{command}{print\_induct\_rules}\hypertarget{command.print-induct-rules}{\hyperlink{command.print-induct-rules}{\mbox{\isa{\isacommand{print{\isacharunderscore}induct{\isacharunderscore}rules}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
1.1116 + \indexdef{}{command}{print\_induct\_rules}\hypertarget{command.print-induct-rules}{\hyperlink{command.print-induct-rules}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}induct{\isaliteral{5F}{\isacharunderscore}}rules}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
1.1117 \indexdef{}{attribute}{cases}\hypertarget{attribute.cases}{\hyperlink{attribute.cases}{\mbox{\isa{cases}}}} & : & \isa{attribute} \\
1.1118 \indexdef{}{attribute}{induct}\hypertarget{attribute.induct}{\hyperlink{attribute.induct}{\mbox{\isa{induct}}}} & : & \isa{attribute} \\
1.1119 \indexdef{}{attribute}{coinduct}\hypertarget{attribute.coinduct}{\hyperlink{attribute.coinduct}{\mbox{\isa{coinduct}}}} & : & \isa{attribute} \\
1.1120 @@ -1468,7 +1468,7 @@
1.1121
1.1122 \begin{description}
1.1123
1.1124 - \item \hyperlink{command.print-induct-rules}{\mbox{\isa{\isacommand{print{\isacharunderscore}induct{\isacharunderscore}rules}}}} prints cases and induct rules
1.1125 + \item \hyperlink{command.print-induct-rules}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}induct{\isaliteral{5F}{\isacharunderscore}}rules}}}} prints cases and induct rules
1.1126 for predicates (or sets) and types of the current context.
1.1127
1.1128 \item \hyperlink{attribute.cases}{\mbox{\isa{cases}}}, \hyperlink{attribute.induct}{\mbox{\isa{induct}}}, and \hyperlink{attribute.coinduct}{\mbox{\isa{coinduct}}} (as attributes) declare rules for reasoning about
1.1129 @@ -1477,12 +1477,12 @@
1.1130 packages of object-logics usually declare emerging cases and
1.1131 induction rules as expected, so users rarely need to intervene.
1.1132
1.1133 - Rules may be deleted via the \isa{{\isachardoublequote}del{\isachardoublequote}} specification, which
1.1134 - covers all of the \isa{{\isachardoublequote}type{\isachardoublequote}}/\isa{{\isachardoublequote}pred{\isachardoublequote}}/\isa{{\isachardoublequote}set{\isachardoublequote}}
1.1135 + Rules may be deleted via the \isa{{\isaliteral{22}{\isachardoublequote}}del{\isaliteral{22}{\isachardoublequote}}} specification, which
1.1136 + covers all of the \isa{{\isaliteral{22}{\isachardoublequote}}type{\isaliteral{22}{\isachardoublequote}}}/\isa{{\isaliteral{22}{\isachardoublequote}}pred{\isaliteral{22}{\isachardoublequote}}}/\isa{{\isaliteral{22}{\isachardoublequote}}set{\isaliteral{22}{\isachardoublequote}}}
1.1137 sub-categories simultaneously. For example, \hyperlink{attribute.cases}{\mbox{\isa{cases}}}~\isa{del} removes any \hyperlink{attribute.cases}{\mbox{\isa{cases}}} rules declared for
1.1138 some type, predicate, or set.
1.1139
1.1140 - Manual rule declarations usually refer to the \hyperlink{attribute.case-names}{\mbox{\isa{case{\isacharunderscore}names}}} and \hyperlink{attribute.params}{\mbox{\isa{params}}} attributes to adjust names of
1.1141 + Manual rule declarations usually refer to the \hyperlink{attribute.case-names}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}names}}} and \hyperlink{attribute.params}{\mbox{\isa{params}}} attributes to adjust names of
1.1142 cases and parameters of a rule; the \hyperlink{attribute.consumes}{\mbox{\isa{consumes}}}
1.1143 declaration is taken care of automatically: \hyperlink{attribute.consumes}{\mbox{\isa{consumes}}}~\isa{{\isadigit{0}}} is specified for ``type'' rules and \hyperlink{attribute.consumes}{\mbox{\isa{consumes}}}~\isa{{\isadigit{1}}} for ``predicate'' / ``set'' rules.
1.1144