1.1 --- a/doc-src/ZF/FOL-eg.txt Fri Aug 15 13:45:39 2003 +0200
1.2 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000
1.3 @@ -1,245 +0,0 @@
1.4 -(**** FOL examples ****)
1.5 -
1.6 -Pretty.setmargin 72; (*existing macros just allow this margin*)
1.7 -print_depth 0;
1.8 -
1.9 -(*** Intuitionistic examples ***)
1.10 -
1.11 -context IFOL.thy;
1.12 -
1.13 -(*Quantifier example from Logic&Computation*)
1.14 -Goal "(EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))";
1.15 -by (resolve_tac [impI] 1);
1.16 -by (resolve_tac [allI] 1);
1.17 -by (resolve_tac [exI] 1);
1.18 -by (eresolve_tac [exE] 1);
1.19 -choplev 2;
1.20 -by (eresolve_tac [exE] 1);
1.21 -by (resolve_tac [exI] 1);
1.22 -by (eresolve_tac [allE] 1);
1.23 -by (assume_tac 1);
1.24 -
1.25 -
1.26 -(*Example of Dyckhoff's method*)
1.27 -Goalw [not_def] "~ ~ ((P-->Q) | (Q-->P))";
1.28 -by (resolve_tac [impI] 1);
1.29 -by (eresolve_tac [disj_impE] 1);
1.30 -by (eresolve_tac [imp_impE] 1);
1.31 -by (eresolve_tac [imp_impE] 1);
1.32 -by (REPEAT (eresolve_tac [FalseE] 2));
1.33 -by (assume_tac 1);
1.34 -
1.35 -
1.36 -
1.37 -
1.38 -
1.39 -(*** Classical examples ***)
1.40 -
1.41 -context FOL.thy;
1.42 -
1.43 -Goal "EX y. ALL x. P(y)-->P(x)";
1.44 -by (resolve_tac [exCI] 1);
1.45 -by (resolve_tac [allI] 1);
1.46 -by (resolve_tac [impI] 1);
1.47 -by (eresolve_tac [allE] 1);
1.48 -prth (allI RSN (2,swap));
1.49 -by (eresolve_tac [it] 1);
1.50 -by (resolve_tac [impI] 1);
1.51 -by (eresolve_tac [notE] 1);
1.52 -by (assume_tac 1);
1.53 -Goal "EX y. ALL x. P(y)-->P(x)";
1.54 -by (Blast_tac 1);
1.55 -
1.56 -
1.57 -
1.58 -- Goal "EX y. ALL x. P(y)-->P(x)";
1.59 -Level 0
1.60 -EX y. ALL x. P(y) --> P(x)
1.61 - 1. EX y. ALL x. P(y) --> P(x)
1.62 -- by (resolve_tac [exCI] 1);
1.63 -Level 1
1.64 -EX y. ALL x. P(y) --> P(x)
1.65 - 1. ALL y. ~(ALL x. P(y) --> P(x)) ==> ALL x. P(?a) --> P(x)
1.66 -- by (resolve_tac [allI] 1);
1.67 -Level 2
1.68 -EX y. ALL x. P(y) --> P(x)
1.69 - 1. !!x. ALL y. ~(ALL x. P(y) --> P(x)) ==> P(?a) --> P(x)
1.70 -- by (resolve_tac [impI] 1);
1.71 -Level 3
1.72 -EX y. ALL x. P(y) --> P(x)
1.73 - 1. !!x. [| ALL y. ~(ALL x. P(y) --> P(x)); P(?a) |] ==> P(x)
1.74 -- by (eresolve_tac [allE] 1);
1.75 -Level 4
1.76 -EX y. ALL x. P(y) --> P(x)
1.77 - 1. !!x. [| P(?a); ~(ALL xa. P(?y3(x)) --> P(xa)) |] ==> P(x)
1.78 -- prth (allI RSN (2,swap));
1.79 -[| ~(ALL x. ?P1(x)); !!x. ~?Q ==> ?P1(x) |] ==> ?Q
1.80 -- by (eresolve_tac [it] 1);
1.81 -Level 5
1.82 -EX y. ALL x. P(y) --> P(x)
1.83 - 1. !!x xa. [| P(?a); ~P(x) |] ==> P(?y3(x)) --> P(xa)
1.84 -- by (resolve_tac [impI] 1);
1.85 -Level 6
1.86 -EX y. ALL x. P(y) --> P(x)
1.87 - 1. !!x xa. [| P(?a); ~P(x); P(?y3(x)) |] ==> P(xa)
1.88 -- by (eresolve_tac [notE] 1);
1.89 -Level 7
1.90 -EX y. ALL x. P(y) --> P(x)
1.91 - 1. !!x xa. [| P(?a); P(?y3(x)) |] ==> P(x)
1.92 -- by (assume_tac 1);
1.93 -Level 8
1.94 -EX y. ALL x. P(y) --> P(x)
1.95 -No subgoals!
1.96 -- Goal "EX y. ALL x. P(y)-->P(x)";
1.97 -Level 0
1.98 -EX y. ALL x. P(y) --> P(x)
1.99 - 1. EX y. ALL x. P(y) --> P(x)
1.100 -- by (best_tac FOL_dup_cs 1);
1.101 -Level 1
1.102 -EX y. ALL x. P(y) --> P(x)
1.103 -No subgoals!
1.104 -
1.105 -
1.106 -(**** finally, the example FOL/ex/if.ML ****)
1.107 -
1.108 -> val prems = goalw if_thy [if_def]
1.109 -# "[| P ==> Q; ~P ==> R |] ==> if(P,Q,R)";
1.110 -Level 0
1.111 -if(P,Q,R)
1.112 - 1. P & Q | ~P & R
1.113 -> by (Classical.fast_tac (FOL_cs addIs prems) 1);
1.114 -Level 1
1.115 -if(P,Q,R)
1.116 -No subgoals!
1.117 -> val ifI = result();
1.118 -
1.119 -
1.120 -> val major::prems = goalw if_thy [if_def]
1.121 -# "[| if(P,Q,R); [| P; Q |] ==> S; [| ~P; R |] ==> S |] ==> S";
1.122 -Level 0
1.123 -S
1.124 - 1. S
1.125 -> by (cut_facts_tac [major] 1);
1.126 -Level 1
1.127 -S
1.128 - 1. P & Q | ~P & R ==> S
1.129 -> by (Classical.fast_tac (FOL_cs addIs prems) 1);
1.130 -Level 2
1.131 -S
1.132 -No subgoals!
1.133 -> val ifE = result();
1.134 -
1.135 -> goal if_thy "if(P, if(Q,A,B), if(Q,C,D)) <-> if(Q, if(P,A,C), if(P,B,D))";
1.136 -Level 0
1.137 -if(P,if(Q,A,B),if(Q,C,D)) <-> if(Q,if(P,A,C),if(P,B,D))
1.138 - 1. if(P,if(Q,A,B),if(Q,C,D)) <-> if(Q,if(P,A,C),if(P,B,D))
1.139 -> by (resolve_tac [iffI] 1);
1.140 -Level 1
1.141 -if(P,if(Q,A,B),if(Q,C,D)) <-> if(Q,if(P,A,C),if(P,B,D))
1.142 - 1. if(P,if(Q,A,B),if(Q,C,D)) ==> if(Q,if(P,A,C),if(P,B,D))
1.143 - 2. if(Q,if(P,A,C),if(P,B,D)) ==> if(P,if(Q,A,B),if(Q,C,D))
1.144 -> by (eresolve_tac [ifE] 1);
1.145 -Level 2
1.146 -if(P,if(Q,A,B),if(Q,C,D)) <-> if(Q,if(P,A,C),if(P,B,D))
1.147 - 1. [| P; if(Q,A,B) |] ==> if(Q,if(P,A,C),if(P,B,D))
1.148 - 2. [| ~P; if(Q,C,D) |] ==> if(Q,if(P,A,C),if(P,B,D))
1.149 - 3. if(Q,if(P,A,C),if(P,B,D)) ==> if(P,if(Q,A,B),if(Q,C,D))
1.150 -> by (eresolve_tac [ifE] 1);
1.151 -Level 3
1.152 -if(P,if(Q,A,B),if(Q,C,D)) <-> if(Q,if(P,A,C),if(P,B,D))
1.153 - 1. [| P; Q; A |] ==> if(Q,if(P,A,C),if(P,B,D))
1.154 - 2. [| P; ~Q; B |] ==> if(Q,if(P,A,C),if(P,B,D))
1.155 - 3. [| ~P; if(Q,C,D) |] ==> if(Q,if(P,A,C),if(P,B,D))
1.156 - 4. if(Q,if(P,A,C),if(P,B,D)) ==> if(P,if(Q,A,B),if(Q,C,D))
1.157 -> by (resolve_tac [ifI] 1);
1.158 -Level 4
1.159 -if(P,if(Q,A,B),if(Q,C,D)) <-> if(Q,if(P,A,C),if(P,B,D))
1.160 - 1. [| P; Q; A; Q |] ==> if(P,A,C)
1.161 - 2. [| P; Q; A; ~Q |] ==> if(P,B,D)
1.162 - 3. [| P; ~Q; B |] ==> if(Q,if(P,A,C),if(P,B,D))
1.163 - 4. [| ~P; if(Q,C,D) |] ==> if(Q,if(P,A,C),if(P,B,D))
1.164 - 5. if(Q,if(P,A,C),if(P,B,D)) ==> if(P,if(Q,A,B),if(Q,C,D))
1.165 -> by (resolve_tac [ifI] 1);
1.166 -Level 5
1.167 -if(P,if(Q,A,B),if(Q,C,D)) <-> if(Q,if(P,A,C),if(P,B,D))
1.168 - 1. [| P; Q; A; Q; P |] ==> A
1.169 - 2. [| P; Q; A; Q; ~P |] ==> C
1.170 - 3. [| P; Q; A; ~Q |] ==> if(P,B,D)
1.171 - 4. [| P; ~Q; B |] ==> if(Q,if(P,A,C),if(P,B,D))
1.172 - 5. [| ~P; if(Q,C,D) |] ==> if(Q,if(P,A,C),if(P,B,D))
1.173 - 6. if(Q,if(P,A,C),if(P,B,D)) ==> if(P,if(Q,A,B),if(Q,C,D))
1.174 -
1.175 -> choplev 0;
1.176 -Level 0
1.177 -if(P,if(Q,A,B),if(Q,C,D)) <-> if(Q,if(P,A,C),if(P,B,D))
1.178 - 1. if(P,if(Q,A,B),if(Q,C,D)) <-> if(Q,if(P,A,C),if(P,B,D))
1.179 -> val if_cs = FOL_cs addSIs [ifI] addSEs[ifE];
1.180 -> by (Classical.fast_tac if_cs 1);
1.181 -Level 1
1.182 -if(P,if(Q,A,B),if(Q,C,D)) <-> if(Q,if(P,A,C),if(P,B,D))
1.183 -No subgoals!
1.184 -> val if_commute = result();
1.185 -
1.186 -> goal if_thy "if(if(P,Q,R), A, B) <-> if(P, if(Q,A,B), if(R,A,B))";
1.187 -Level 0
1.188 -if(if(P,Q,R),A,B) <-> if(P,if(Q,A,B),if(R,A,B))
1.189 - 1. if(if(P,Q,R),A,B) <-> if(P,if(Q,A,B),if(R,A,B))
1.190 -> by (Classical.fast_tac if_cs 1);
1.191 -Level 1
1.192 -if(if(P,Q,R),A,B) <-> if(P,if(Q,A,B),if(R,A,B))
1.193 -No subgoals!
1.194 -> val nested_ifs = result();
1.195 -
1.196 -
1.197 -> choplev 0;
1.198 -Level 0
1.199 -if(if(P,Q,R),A,B) <-> if(P,if(Q,A,B),if(R,A,B))
1.200 - 1. if(if(P,Q,R),A,B) <-> if(P,if(Q,A,B),if(R,A,B))
1.201 -> by (rewrite_goals_tac [if_def]);
1.202 -Level 1
1.203 -if(if(P,Q,R),A,B) <-> if(P,if(Q,A,B),if(R,A,B))
1.204 - 1. (P & Q | ~P & R) & A | ~(P & Q | ~P & R) & B <->
1.205 - P & (Q & A | ~Q & B) | ~P & (R & A | ~R & B)
1.206 -> by (Classical.fast_tac FOL_cs 1);
1.207 -Level 2
1.208 -if(if(P,Q,R),A,B) <-> if(P,if(Q,A,B),if(R,A,B))
1.209 -No subgoals!
1.210 -
1.211 -
1.212 -> goal if_thy "if(if(P,Q,R), A, B) <-> if(P, if(Q,A,B), if(R,B,A))";
1.213 -Level 0
1.214 -if(if(P,Q,R),A,B) <-> if(P,if(Q,A,B),if(R,B,A))
1.215 - 1. if(if(P,Q,R),A,B) <-> if(P,if(Q,A,B),if(R,B,A))
1.216 -> by (REPEAT (Classical.step_tac if_cs 1));
1.217 -Level 1
1.218 -if(if(P,Q,R),A,B) <-> if(P,if(Q,A,B),if(R,B,A))
1.219 - 1. [| A; ~P; R; ~P; R |] ==> B
1.220 - 2. [| B; ~P; ~R; ~P; ~R |] ==> A
1.221 - 3. [| ~P; R; B; ~P; R |] ==> A
1.222 - 4. [| ~P; ~R; A; ~B; ~P |] ==> R
1.223 -
1.224 -> choplev 0;
1.225 -Level 0
1.226 -if(if(P,Q,R),A,B) <-> if(P,if(Q,A,B),if(R,B,A))
1.227 - 1. if(if(P,Q,R),A,B) <-> if(P,if(Q,A,B),if(R,B,A))
1.228 -> by (rewrite_goals_tac [if_def]);
1.229 -Level 1
1.230 -if(if(P,Q,R),A,B) <-> if(P,if(Q,A,B),if(R,B,A))
1.231 - 1. (P & Q | ~P & R) & A | ~(P & Q | ~P & R) & B <->
1.232 - P & (Q & A | ~Q & B) | ~P & (R & B | ~R & A)
1.233 -> by (Classical.fast_tac FOL_cs 1);
1.234 -by: tactic failed
1.235 -Exception- ERROR raised
1.236 -Exception failure raised
1.237 -
1.238 -> by (REPEAT (Classical.step_tac FOL_cs 1));
1.239 -Level 2
1.240 -if(if(P,Q,R),A,B) <-> if(P,if(Q,A,B),if(R,B,A))
1.241 - 1. [| A; ~P; R; ~P; R; ~False |] ==> B
1.242 - 2. [| A; ~P; R; R; ~False; ~B; ~B |] ==> Q
1.243 - 3. [| B; ~P; ~R; ~P; ~A |] ==> R
1.244 - 4. [| B; ~P; ~R; ~Q; ~A |] ==> R
1.245 - 5. [| B; ~R; ~P; ~A; ~R; Q; ~False |] ==> A
1.246 - 6. [| ~P; R; B; ~P; R; ~False |] ==> A
1.247 - 7. [| ~P; ~R; A; ~B; ~R |] ==> P
1.248 - 8. [| ~P; ~R; A; ~B; ~R |] ==> Q
2.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
2.2 +++ b/doc-src/ZF/FOL_examples.thy Tue Aug 19 13:53:58 2003 +0200
2.3 @@ -0,0 +1,34 @@
2.4 +header{*Examples of Classical Reasoning*}
2.5 +
2.6 +theory FOL_examples = FOL:
2.7 +
2.8 +lemma "EX y. ALL x. P(y)-->P(x)"
2.9 + --{* @{subgoals[display,indent=0,margin=65]} *}
2.10 +apply (rule exCI)
2.11 + --{* @{subgoals[display,indent=0,margin=65]} *}
2.12 +apply (rule allI)
2.13 + --{* @{subgoals[display,indent=0,margin=65]} *}
2.14 +apply (rule impI)
2.15 + --{* @{subgoals[display,indent=0,margin=65]} *}
2.16 +apply (erule allE)
2.17 + --{* @{subgoals[display,indent=0,margin=65]} *}
2.18 +txt{*see below for @{text allI} combined with @{text swap}*}
2.19 +apply (erule allI [THEN [2] swap])
2.20 + --{* @{subgoals[display,indent=0,margin=65]} *}
2.21 +apply (rule impI)
2.22 + --{* @{subgoals[display,indent=0,margin=65]} *}
2.23 +apply (erule notE)
2.24 + --{* @{subgoals[display,indent=0,margin=65]} *}
2.25 +apply assumption
2.26 +done
2.27 +
2.28 +text {*
2.29 +@{thm[display] allI [THEN [2] swap]}
2.30 +*}
2.31 +
2.32 +lemma "EX y. ALL x. P(y)-->P(x)"
2.33 +by blast
2.34 +
2.35 +end
2.36 +
2.37 +
3.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
3.2 +++ b/doc-src/ZF/IFOL_examples.thy Tue Aug 19 13:53:58 2003 +0200
3.3 @@ -0,0 +1,58 @@
3.4 +header{*Examples of Intuitionistic Reasoning*}
3.5 +
3.6 +theory IFOL_examples = IFOL:
3.7 +
3.8 +text{*Quantifier example from the book Logic and Computation*}
3.9 +lemma "(EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))"
3.10 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.11 +apply (rule impI)
3.12 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.13 +apply (rule allI)
3.14 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.15 +apply (rule exI)
3.16 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.17 +apply (erule exE)
3.18 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.19 +apply (erule allE)
3.20 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.21 +txt{*Now @{text "apply assumption"} fails*}
3.22 +oops
3.23 +
3.24 +text{*Trying again, with the same first two steps*}
3.25 +lemma "(EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))"
3.26 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.27 +apply (rule impI)
3.28 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.29 +apply (rule allI)
3.30 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.31 +apply (erule exE)
3.32 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.33 +apply (rule exI)
3.34 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.35 +apply (erule allE)
3.36 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.37 +apply assumption
3.38 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.39 +done
3.40 +
3.41 +lemma "(EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))"
3.42 +by (tactic {*IntPr.fast_tac 1*})
3.43 +
3.44 +text{*Example of Dyckhoff's method*}
3.45 +lemma "~ ~ ((P-->Q) | (Q-->P))"
3.46 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.47 +apply (unfold not_def)
3.48 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.49 +apply (rule impI)
3.50 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.51 +apply (erule disj_impE)
3.52 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.53 +apply (erule imp_impE)
3.54 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.55 + apply (erule imp_impE)
3.56 + --{* @{subgoals[display,indent=0,margin=65]} *}
3.57 +apply assumption
3.58 +apply (erule FalseE)+
3.59 +done
3.60 +
3.61 +end
4.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
4.2 +++ b/doc-src/ZF/IsaMakefile Tue Aug 19 13:53:58 2003 +0200
4.3 @@ -0,0 +1,50 @@
4.4 +#
4.5 +# IsaMakefile to build the examples for the FOL and ZF manual
4.6 +#
4.7 +
4.8 +## targets
4.9 +
4.10 +default: ZF-examples styles
4.11 +images:
4.12 +test:
4.13 +all: default
4.14 +
4.15 +
4.16 +## global settings
4.17 +
4.18 +SRC = $(ISABELLE_HOME)/src
4.19 +OUT = $(ISABELLE_OUTPUT)
4.20 +LOG = $(OUT)/log
4.21 +OPTIONS = -m brackets -i true -d "" -D document
4.22 +USEDIR = @$(ISATOOL) usedir $(OPTIONS) $(OUT)/ZF
4.23 +
4.24 +
4.25 +## ZF
4.26 +
4.27 +ZF:
4.28 + @cd $(SRC)/ZF; $(ISATOOL) make ZF
4.29 +
4.30 +styles:
4.31 + @rm -f isabelle.sty
4.32 + @rm -f isabellesym.sty
4.33 + @rm -f pdfsetup.sty
4.34 + @$(ISATOOL) latex -o sty >/dev/null
4.35 + @rm -f pdfsetup.sty
4.36 + @rm -f document/isabelle.sty
4.37 + @rm -f document/isabellesym.sty
4.38 + @rm -f document/pdfsetup.sty
4.39 + @rm -f document/session.tex
4.40 +
4.41 +
4.42 +## ZF-examples
4.43 +
4.44 +ZF-examples: ZF $(LOG)/ZF-examples.gz
4.45 +
4.46 +$(LOG)/ZF-examples.gz: $(OUT)/ZF \
4.47 + FOL_examples.thy IFOL_examples.thy ZF_examples.thy If.thy ROOT.ML
4.48 + @$(USEDIR) .
4.49 +
4.50 +## clean
4.51 +
4.52 +clean:
4.53 + @rm -f $(LOG)/ZF-examples.gz document/*.tex
5.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
5.2 +++ b/doc-src/ZF/ROOT.ML Tue Aug 19 13:53:58 2003 +0200
5.3 @@ -0,0 +1,5 @@
5.4 +(* ID: $Id$ *)
5.5 +use_thy "IFOL_examples";
5.6 +use_thy "FOL_examples";
5.7 +use_thy "ZF_examples";
5.8 +use_thy "If";
6.1 --- a/doc-src/ZF/ZF-eg.txt Fri Aug 15 13:45:39 2003 +0200
6.2 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000
6.3 @@ -1,230 +0,0 @@
6.4 -(**** ZF examples ****)
6.5 -
6.6 -Pretty.setmargin 72; (*existing macros just allow this margin*)
6.7 -print_depth 0;
6.8 -
6.9 -(*** Powerset example ***)
6.10 -
6.11 -val [prem] = goal ZF.thy "A<=B ==> Pow(A) <= Pow(B)";
6.12 -by (resolve_tac [subsetI] 1);
6.13 -by (resolve_tac [PowI] 1);
6.14 -by (dresolve_tac [PowD] 1);
6.15 -by (eresolve_tac [subset_trans] 1);
6.16 -by (resolve_tac [prem] 1);
6.17 -val Pow_mono = result();
6.18 -
6.19 -goal ZF.thy "Pow(A Int B) = Pow(A) Int Pow(B)";
6.20 -by (resolve_tac [equalityI] 1);
6.21 -by (resolve_tac [Int_greatest] 1);
6.22 -by (resolve_tac [Int_lower1 RS Pow_mono] 1);
6.23 -by (resolve_tac [Int_lower2 RS Pow_mono] 1);
6.24 -by (resolve_tac [subsetI] 1);
6.25 -by (eresolve_tac [IntE] 1);
6.26 -by (resolve_tac [PowI] 1);
6.27 -by (REPEAT (dresolve_tac [PowD] 1));
6.28 -by (resolve_tac [Int_greatest] 1);
6.29 -by (REPEAT (assume_tac 1));
6.30 -choplev 0;
6.31 -by (fast_tac (ZF_cs addIs [equalityI]) 1);
6.32 -
6.33 -Goal "C<=D ==> Union(C) <= Union(D)";
6.34 -by (resolve_tac [subsetI] 1);
6.35 -by (eresolve_tac [UnionE] 1);
6.36 -by (resolve_tac [UnionI] 1);
6.37 -by (eresolve_tac [subsetD] 1);
6.38 -by (assume_tac 1);
6.39 -by (assume_tac 1);
6.40 -choplev 0;
6.41 -by (resolve_tac [Union_least] 1);
6.42 -by (resolve_tac [Union_upper] 1);
6.43 -by (eresolve_tac [subsetD] 1);
6.44 -
6.45 -
6.46 -val prems = goal ZF.thy
6.47 - "[| a:A; f: A->B; g: C->D; A Int C = 0 |] ==> \
6.48 -\ (f Un g)`a = f`a";
6.49 -by (resolve_tac [apply_equality] 1);
6.50 -by (resolve_tac [UnI1] 1);
6.51 -by (resolve_tac [apply_Pair] 1);
6.52 -by (resolve_tac prems 1);
6.53 -by (resolve_tac prems 1);
6.54 -by (resolve_tac [fun_disjoint_Un] 1);
6.55 -by (resolve_tac prems 1);
6.56 -by (resolve_tac prems 1);
6.57 -by (resolve_tac prems 1);
6.58 -
6.59 -
6.60 -Goal "[| a:A; f: A->B; g: C->D; A Int C = 0 |] ==> \
6.61 -\ (f Un g)`a = f`a";
6.62 -by (resolve_tac [apply_equality] 1);
6.63 -by (resolve_tac [UnI1] 1);
6.64 -by (resolve_tac [apply_Pair] 1);
6.65 -by (assume_tac 1);
6.66 -by (assume_tac 1);
6.67 -by (resolve_tac [fun_disjoint_Un] 1);
6.68 -by (assume_tac 1);
6.69 -by (assume_tac 1);
6.70 -by (assume_tac 1);
6.71 -
6.72 -
6.73 -
6.74 -
6.75 -goal ZF.thy "f``(UN x:A. B(x)) = (UN x:A. f``B(x))";
6.76 -by (resolve_tac [equalityI] 1);
6.77 -by (resolve_tac [subsetI] 1);
6.78 -fe imageE;
6.79 -
6.80 -
6.81 -goal ZF.thy "(UN x:C. A(x) Int B) = (UN x:C. A(x)) Int B";
6.82 -by (resolve_tac [equalityI] 1);
6.83 -by (resolve_tac [Int_greatest] 1);
6.84 -fr UN_mono;
6.85 -by (resolve_tac [Int_lower1] 1);
6.86 -fr UN_least;
6.87 -????
6.88 -
6.89 -
6.90 -> goal ZF.thy "Pow(A Int B) = Pow(A) Int Pow(B)";
6.91 -Level 0
6.92 -Pow(A Int B) = Pow(A) Int Pow(B)
6.93 - 1. Pow(A Int B) = Pow(A) Int Pow(B)
6.94 -> by (resolve_tac [equalityI] 1);
6.95 -Level 1
6.96 -Pow(A Int B) = Pow(A) Int Pow(B)
6.97 - 1. Pow(A Int B) <= Pow(A) Int Pow(B)
6.98 - 2. Pow(A) Int Pow(B) <= Pow(A Int B)
6.99 -> by (resolve_tac [Int_greatest] 1);
6.100 -Level 2
6.101 -Pow(A Int B) = Pow(A) Int Pow(B)
6.102 - 1. Pow(A Int B) <= Pow(A)
6.103 - 2. Pow(A Int B) <= Pow(B)
6.104 - 3. Pow(A) Int Pow(B) <= Pow(A Int B)
6.105 -> by (resolve_tac [Int_lower1 RS Pow_mono] 1);
6.106 -Level 3
6.107 -Pow(A Int B) = Pow(A) Int Pow(B)
6.108 - 1. Pow(A Int B) <= Pow(B)
6.109 - 2. Pow(A) Int Pow(B) <= Pow(A Int B)
6.110 -> by (resolve_tac [Int_lower2 RS Pow_mono] 1);
6.111 -Level 4
6.112 -Pow(A Int B) = Pow(A) Int Pow(B)
6.113 - 1. Pow(A) Int Pow(B) <= Pow(A Int B)
6.114 -> by (resolve_tac [subsetI] 1);
6.115 -Level 5
6.116 -Pow(A Int B) = Pow(A) Int Pow(B)
6.117 - 1. !!x. x : Pow(A) Int Pow(B) ==> x : Pow(A Int B)
6.118 -> by (eresolve_tac [IntE] 1);
6.119 -Level 6
6.120 -Pow(A Int B) = Pow(A) Int Pow(B)
6.121 - 1. !!x. [| x : Pow(A); x : Pow(B) |] ==> x : Pow(A Int B)
6.122 -> by (resolve_tac [PowI] 1);
6.123 -Level 7
6.124 -Pow(A Int B) = Pow(A) Int Pow(B)
6.125 - 1. !!x. [| x : Pow(A); x : Pow(B) |] ==> x <= A Int B
6.126 -> by (REPEAT (dresolve_tac [PowD] 1));
6.127 -Level 8
6.128 -Pow(A Int B) = Pow(A) Int Pow(B)
6.129 - 1. !!x. [| x <= A; x <= B |] ==> x <= A Int B
6.130 -> by (resolve_tac [Int_greatest] 1);
6.131 -Level 9
6.132 -Pow(A Int B) = Pow(A) Int Pow(B)
6.133 - 1. !!x. [| x <= A; x <= B |] ==> x <= A
6.134 - 2. !!x. [| x <= A; x <= B |] ==> x <= B
6.135 -> by (REPEAT (assume_tac 1));
6.136 -Level 10
6.137 -Pow(A Int B) = Pow(A) Int Pow(B)
6.138 -No subgoals!
6.139 -> choplev 0;
6.140 -Level 0
6.141 -Pow(A Int B) = Pow(A) Int Pow(B)
6.142 - 1. Pow(A Int B) = Pow(A) Int Pow(B)
6.143 -> by (fast_tac (ZF_cs addIs [equalityI]) 1);
6.144 -Level 1
6.145 -Pow(A Int B) = Pow(A) Int Pow(B)
6.146 -No subgoals!
6.147 -
6.148 -
6.149 -
6.150 -
6.151 -> val [prem] = goal ZF.thy "C<=D ==> Union(C) <= Union(D)";
6.152 -Level 0
6.153 -Union(C) <= Union(D)
6.154 - 1. Union(C) <= Union(D)
6.155 -> by (resolve_tac [subsetI] 1);
6.156 -Level 1
6.157 -Union(C) <= Union(D)
6.158 - 1. !!x. x : Union(C) ==> x : Union(D)
6.159 -> by (eresolve_tac [UnionE] 1);
6.160 -Level 2
6.161 -Union(C) <= Union(D)
6.162 - 1. !!x B. [| x : B; B : C |] ==> x : Union(D)
6.163 -> by (resolve_tac [UnionI] 1);
6.164 -Level 3
6.165 -Union(C) <= Union(D)
6.166 - 1. !!x B. [| x : B; B : C |] ==> ?B2(x,B) : D
6.167 - 2. !!x B. [| x : B; B : C |] ==> x : ?B2(x,B)
6.168 -> by (resolve_tac [prem RS subsetD] 1);
6.169 -Level 4
6.170 -Union(C) <= Union(D)
6.171 - 1. !!x B. [| x : B; B : C |] ==> ?B2(x,B) : C
6.172 - 2. !!x B. [| x : B; B : C |] ==> x : ?B2(x,B)
6.173 -> by (assume_tac 1);
6.174 -Level 5
6.175 -Union(C) <= Union(D)
6.176 - 1. !!x B. [| x : B; B : C |] ==> x : B
6.177 -> by (assume_tac 1);
6.178 -Level 6
6.179 -Union(C) <= Union(D)
6.180 -No subgoals!
6.181 -
6.182 -
6.183 -
6.184 -> val prems = goal ZF.thy
6.185 -# "[| a:A; f: A->B; g: C->D; A Int C = 0 |] ==> \
6.186 -# \ (f Un g)`a = f`a";
6.187 -Level 0
6.188 -(f Un g) ` a = f ` a
6.189 - 1. (f Un g) ` a = f ` a
6.190 -> by (resolve_tac [apply_equality] 1);
6.191 -Level 1
6.192 -(f Un g) ` a = f ` a
6.193 - 1. <a,f ` a> : f Un g
6.194 - 2. f Un g : (PROD x:?A. ?B(x))
6.195 -> by (resolve_tac [UnI1] 1);
6.196 -Level 2
6.197 -(f Un g) ` a = f ` a
6.198 - 1. <a,f ` a> : f
6.199 - 2. f Un g : (PROD x:?A. ?B(x))
6.200 -> by (resolve_tac [apply_Pair] 1);
6.201 -Level 3
6.202 -(f Un g) ` a = f ` a
6.203 - 1. f : (PROD x:?A2. ?B2(x))
6.204 - 2. a : ?A2
6.205 - 3. f Un g : (PROD x:?A. ?B(x))
6.206 -> by (resolve_tac prems 1);
6.207 -Level 4
6.208 -(f Un g) ` a = f ` a
6.209 - 1. a : A
6.210 - 2. f Un g : (PROD x:?A. ?B(x))
6.211 -> by (resolve_tac prems 1);
6.212 -Level 5
6.213 -(f Un g) ` a = f ` a
6.214 - 1. f Un g : (PROD x:?A. ?B(x))
6.215 -> by (resolve_tac [fun_disjoint_Un] 1);
6.216 -Level 6
6.217 -(f Un g) ` a = f ` a
6.218 - 1. f : ?A3 -> ?B3
6.219 - 2. g : ?C3 -> ?D3
6.220 - 3. ?A3 Int ?C3 = 0
6.221 -> by (resolve_tac prems 1);
6.222 -Level 7
6.223 -(f Un g) ` a = f ` a
6.224 - 1. g : ?C3 -> ?D3
6.225 - 2. A Int ?C3 = 0
6.226 -> by (resolve_tac prems 1);
6.227 -Level 8
6.228 -(f Un g) ` a = f ` a
6.229 - 1. A Int C = 0
6.230 -> by (resolve_tac prems 1);
6.231 -Level 9
6.232 -(f Un g) ` a = f ` a
6.233 -No subgoals!
7.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
7.2 +++ b/doc-src/ZF/ZF_examples.thy Tue Aug 19 13:53:58 2003 +0200
7.3 @@ -0,0 +1,121 @@
7.4 +header{*Examples of Reasoning in ZF Set Theory*}
7.5 +
7.6 +theory ZF_examples = Main_ZFC:
7.7 +
7.8 +subsection {* Binary Trees *}
7.9 +
7.10 +consts
7.11 + bt :: "i => i"
7.12 +
7.13 +datatype "bt(A)" =
7.14 + Lf | Br ("a \<in> A", "t1 \<in> bt(A)", "t2 \<in> bt(A)")
7.15 +
7.16 +declare bt.intros [simp]
7.17 +
7.18 +text{*Induction via tactic emulation*}
7.19 +lemma Br_neq_left [rule_format]: "l \<in> bt(A) ==> \<forall>x r. Br(x, l, r) \<noteq> l"
7.20 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.21 + apply (induct_tac l)
7.22 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.23 + apply auto
7.24 + done
7.25 +
7.26 +(*
7.27 + apply (Inductive.case_tac l)
7.28 + apply (tactic {*exhaust_tac "l" 1*})
7.29 +*)
7.30 +
7.31 +text{*The new induction method, which I don't understand*}
7.32 +lemma Br_neq_left': "l \<in> bt(A) ==> (!!x r. Br(x, l, r) \<noteq> l)"
7.33 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.34 + apply (induct set: bt)
7.35 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.36 + apply auto
7.37 + done
7.38 +
7.39 +lemma Br_iff: "Br(a, l, r) = Br(a', l', r') <-> a = a' & l = l' & r = r'"
7.40 + -- "Proving a freeness theorem."
7.41 + by (blast elim!: bt.free_elims)
7.42 +
7.43 +inductive_cases BrE: "Br(a, l, r) \<in> bt(A)"
7.44 + -- "An elimination rule, for type-checking."
7.45 +
7.46 +text {*
7.47 +@{thm[display] BrE[no_vars]}
7.48 +\rulename{BrE}
7.49 +*};
7.50 +
7.51 +subsection{*Powerset example*}
7.52 +
7.53 +lemma Pow_mono: "A<=B ==> Pow(A) <= Pow(B)"
7.54 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.55 +apply (rule subsetI)
7.56 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.57 +apply (rule PowI)
7.58 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.59 +apply (drule PowD)
7.60 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.61 +apply (erule subset_trans, assumption)
7.62 +done
7.63 +
7.64 +lemma "Pow(A Int B) = Pow(A) Int Pow(B)"
7.65 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.66 +apply (rule equalityI)
7.67 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.68 +apply (rule Int_greatest)
7.69 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.70 +apply (rule Int_lower1 [THEN Pow_mono])
7.71 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.72 +apply (rule Int_lower2 [THEN Pow_mono])
7.73 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.74 +apply (rule subsetI)
7.75 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.76 +apply (erule IntE)
7.77 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.78 +apply (rule PowI)
7.79 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.80 +apply (drule PowD)+
7.81 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.82 +apply (rule Int_greatest, assumption+)
7.83 +done
7.84 +
7.85 +text{*Trying again from the beginning in order to use @{text blast}*}
7.86 +lemma "Pow(A Int B) = Pow(A) Int Pow(B)"
7.87 +by blast
7.88 +
7.89 +
7.90 +lemma "C<=D ==> Union(C) <= Union(D)"
7.91 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.92 +apply (rule subsetI)
7.93 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.94 +apply (erule UnionE)
7.95 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.96 +apply (rule UnionI)
7.97 +apply (erule subsetD, assumption, assumption)
7.98 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.99 +done
7.100 +
7.101 +text{*Trying again from the beginning in order to prove from the definitions*}
7.102 +
7.103 +lemma "C<=D ==> Union(C) <= Union(D)"
7.104 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.105 +apply (rule Union_least)
7.106 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.107 +apply (rule Union_upper)
7.108 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.109 +apply (erule subsetD, assumption)
7.110 +done
7.111 +
7.112 +
7.113 +lemma "[| a:A; f: A->B; g: C->D; A Int C = 0 |] ==> (f Un g)`a = f`a"
7.114 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.115 +apply (rule apply_equality)
7.116 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.117 +apply (rule UnI1)
7.118 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.119 +apply (rule apply_Pair, assumption+)
7.120 + --{* @{subgoals[display,indent=0,margin=65]} *}
7.121 +apply (rule fun_disjoint_Un, assumption+)
7.122 +done
7.123 +
7.124 +end
8.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
8.2 +++ b/doc-src/ZF/isabelle.sty Tue Aug 19 13:53:58 2003 +0200
8.3 @@ -0,0 +1,157 @@
8.4 +%%
8.5 +%% Author: Markus Wenzel, TU Muenchen
8.6 +%% License: GPL (GNU GENERAL PUBLIC LICENSE)
8.7 +%%
8.8 +%% macros for Isabelle generated LaTeX output
8.9 +%%
8.10 +
8.11 +%%% Simple document preparation (based on theory token language and symbols)
8.12 +
8.13 +% isabelle environments
8.14 +
8.15 +\newcommand{\isabellecontext}{UNKNOWN}
8.16 +
8.17 +\newcommand{\isastyle}{\small\tt\slshape}
8.18 +\newcommand{\isastyleminor}{\small\tt\slshape}
8.19 +\newcommand{\isastylescript}{\footnotesize\tt\slshape}
8.20 +\newcommand{\isastyletext}{\normalsize\rm}
8.21 +\newcommand{\isastyletxt}{\rm}
8.22 +\newcommand{\isastylecmt}{\rm}
8.23 +
8.24 +%symbol markup -- \emph achieves decent spacing via italic corrections
8.25 +\newcommand{\isamath}[1]{\emph{$#1$}}
8.26 +\newcommand{\isatext}[1]{\emph{#1}}
8.27 +\newcommand{\isascriptstyle}{\def\isamath##1{##1}\def\isatext##1{\mbox{\isastylescript##1}}}
8.28 +\newcommand{\isactrlsub}[1]{\emph{\isascriptstyle${}\sb{#1}$}}
8.29 +\newcommand{\isactrlsup}[1]{\emph{\isascriptstyle${}\sp{#1}$}}
8.30 +\newcommand{\isactrlbold}[1]{{\bfseries\upshape\boldmath#1}}
8.31 +
8.32 +\newdimen\isa@parindent\newdimen\isa@parskip
8.33 +
8.34 +\newenvironment{isabellebody}{%
8.35 +\isamarkuptrue\par%
8.36 +\isa@parindent\parindent\parindent0pt%
8.37 +\isa@parskip\parskip\parskip0pt%
8.38 +\isastyle}{\par}
8.39 +
8.40 +\newenvironment{isabelle}
8.41 +{\begin{trivlist}\begin{isabellebody}\item\relax}
8.42 +{\end{isabellebody}\end{trivlist}}
8.43 +
8.44 +\newcommand{\isa}[1]{\emph{\isastyleminor #1}}
8.45 +
8.46 +\newcommand{\isaindent}[1]{\hphantom{#1}}
8.47 +\newcommand{\isanewline}{\mbox{}\par\mbox{}}
8.48 +\newcommand{\isadigit}[1]{#1}
8.49 +
8.50 +\chardef\isacharbang=`\!
8.51 +\chardef\isachardoublequote=`\"
8.52 +\chardef\isacharhash=`\#
8.53 +\chardef\isachardollar=`\$
8.54 +\chardef\isacharpercent=`\%
8.55 +\chardef\isacharampersand=`\&
8.56 +\chardef\isacharprime=`\'
8.57 +\chardef\isacharparenleft=`\(
8.58 +\chardef\isacharparenright=`\)
8.59 +\chardef\isacharasterisk=`\*
8.60 +\chardef\isacharplus=`\+
8.61 +\chardef\isacharcomma=`\,
8.62 +\chardef\isacharminus=`\-
8.63 +\chardef\isachardot=`\.
8.64 +\chardef\isacharslash=`\/
8.65 +\chardef\isacharcolon=`\:
8.66 +\chardef\isacharsemicolon=`\;
8.67 +\chardef\isacharless=`\<
8.68 +\chardef\isacharequal=`\=
8.69 +\chardef\isachargreater=`\>
8.70 +\chardef\isacharquery=`\?
8.71 +\chardef\isacharat=`\@
8.72 +\chardef\isacharbrackleft=`\[
8.73 +\chardef\isacharbackslash=`\\
8.74 +\chardef\isacharbrackright=`\]
8.75 +\chardef\isacharcircum=`\^
8.76 +\chardef\isacharunderscore=`\_
8.77 +\chardef\isacharbackquote=`\`
8.78 +\chardef\isacharbraceleft=`\{
8.79 +\chardef\isacharbar=`\|
8.80 +\chardef\isacharbraceright=`\}
8.81 +\chardef\isachartilde=`\~
8.82 +
8.83 +
8.84 +% keyword and section markup
8.85 +
8.86 +\newcommand{\isakeywordcharunderscore}{\_}
8.87 +\newcommand{\isakeyword}[1]
8.88 +{\emph{\bf\def\isachardot{.}\def\isacharunderscore{\isakeywordcharunderscore}%
8.89 +\def\isacharbraceleft{\{}\def\isacharbraceright{\}}#1}}
8.90 +\newcommand{\isacommand}[1]{\isakeyword{#1}}
8.91 +
8.92 +\newcommand{\isamarkupheader}[1]{\section{#1}}
8.93 +\newcommand{\isamarkupchapter}[1]{\chapter{#1}}
8.94 +\newcommand{\isamarkupsection}[1]{\section{#1}}
8.95 +\newcommand{\isamarkupsubsection}[1]{\subsection{#1}}
8.96 +\newcommand{\isamarkupsubsubsection}[1]{\subsubsection{#1}}
8.97 +\newcommand{\isamarkupsect}[1]{\section{#1}}
8.98 +\newcommand{\isamarkupsubsect}[1]{\subsection{#1}}
8.99 +\newcommand{\isamarkupsubsubsect}[1]{\subsubsection{#1}}
8.100 +
8.101 +\newif\ifisamarkup
8.102 +\newcommand{\isabeginpar}{\par\ifisamarkup\relax\else\medskip\fi}
8.103 +\newcommand{\isaendpar}{\par\medskip}
8.104 +\newenvironment{isapar}{\parindent\isa@parindent\parskip\isa@parskip\isabeginpar}{\isaendpar}
8.105 +\newenvironment{isamarkuptext}{\isastyletext\begin{isapar}}{\end{isapar}}
8.106 +\newenvironment{isamarkuptxt}{\isastyletxt\begin{isapar}}{\end{isapar}}
8.107 +\newcommand{\isamarkupcmt}[1]{{\isastylecmt--- #1}}
8.108 +
8.109 +
8.110 +% alternative styles
8.111 +
8.112 +\newcommand{\isabellestyle}{}
8.113 +\def\isabellestyle#1{\csname isabellestyle#1\endcsname}
8.114 +
8.115 +\newcommand{\isabellestylett}{%
8.116 +\renewcommand{\isastyle}{\small\tt}%
8.117 +\renewcommand{\isastyleminor}{\small\tt}%
8.118 +\renewcommand{\isastylescript}{\footnotesize\tt}%
8.119 +}
8.120 +\newcommand{\isabellestyleit}{%
8.121 +\renewcommand{\isastyle}{\small\it}%
8.122 +\renewcommand{\isastyleminor}{\it}%
8.123 +\renewcommand{\isastylescript}{\footnotesize\it}%
8.124 +\renewcommand{\isakeywordcharunderscore}{\mbox{-}}%
8.125 +\renewcommand{\isacharbang}{\isamath{!}}%
8.126 +\renewcommand{\isachardoublequote}{}%
8.127 +\renewcommand{\isacharhash}{\isamath{\#}}%
8.128 +\renewcommand{\isachardollar}{\isamath{\$}}%
8.129 +\renewcommand{\isacharpercent}{\isamath{\%}}%
8.130 +\renewcommand{\isacharampersand}{\isamath{\&}}%
8.131 +\renewcommand{\isacharprime}{\isamath{\mskip2mu{'}\mskip-2mu}}%
8.132 +\renewcommand{\isacharparenleft}{\isamath{(}}%
8.133 +\renewcommand{\isacharparenright}{\isamath{)}}%
8.134 +\renewcommand{\isacharasterisk}{\isamath{*}}%
8.135 +\renewcommand{\isacharplus}{\isamath{+}}%
8.136 +\renewcommand{\isacharcomma}{\isamath{\mathord,}}%
8.137 +\renewcommand{\isacharminus}{\isamath{-}}%
8.138 +\renewcommand{\isachardot}{\isamath{\mathord.}}%
8.139 +\renewcommand{\isacharslash}{\isamath{/}}%
8.140 +\renewcommand{\isacharcolon}{\isamath{\mathord:}}%
8.141 +\renewcommand{\isacharsemicolon}{\isamath{\mathord;}}%
8.142 +\renewcommand{\isacharless}{\isamath{<}}%
8.143 +\renewcommand{\isacharequal}{\isamath{=}}%
8.144 +\renewcommand{\isachargreater}{\isamath{>}}%
8.145 +\renewcommand{\isacharat}{\isamath{@}}%
8.146 +\renewcommand{\isacharbrackleft}{\isamath{[}}%
8.147 +\renewcommand{\isacharbrackright}{\isamath{]}}%
8.148 +\renewcommand{\isacharunderscore}{\mbox{-}}%
8.149 +\renewcommand{\isacharbraceleft}{\isamath{\{}}%
8.150 +\renewcommand{\isacharbar}{\isamath{\mid}}%
8.151 +\renewcommand{\isacharbraceright}{\isamath{\}}}%
8.152 +\renewcommand{\isachartilde}{\isamath{{}\sp{\sim}}}%
8.153 +}
8.154 +
8.155 +\newcommand{\isabellestylesl}{%
8.156 +\isabellestyleit%
8.157 +\renewcommand{\isastyle}{\small\sl}%
8.158 +\renewcommand{\isastyleminor}{\sl}%
8.159 +\renewcommand{\isastylescript}{\footnotesize\sl}%
8.160 +}
9.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
9.2 +++ b/doc-src/ZF/isabellesym.sty Tue Aug 19 13:53:58 2003 +0200
9.3 @@ -0,0 +1,354 @@
9.4 +%%
9.5 +%% Author: Markus Wenzel, TU Muenchen
9.6 +%% License: GPL (GNU GENERAL PUBLIC LICENSE)
9.7 +%%
9.8 +%% definitions of standard Isabelle symbols
9.9 +%%
9.10 +
9.11 +% symbol definitions
9.12 +
9.13 +\newcommand{\isasymzero}{\isamath{\mathbf{0}}} %requires amssym
9.14 +\newcommand{\isasymone}{\isamath{\mathbf{1}}} %requires amssym
9.15 +\newcommand{\isasymtwo}{\isamath{\mathbf{2}}} %requires amssym
9.16 +\newcommand{\isasymthree}{\isamath{\mathbf{3}}} %requires amssym
9.17 +\newcommand{\isasymfour}{\isamath{\mathbf{4}}} %requires amssym
9.18 +\newcommand{\isasymfive}{\isamath{\mathbf{5}}} %requires amssym
9.19 +\newcommand{\isasymsix}{\isamath{\mathbf{6}}} %requires amssym
9.20 +\newcommand{\isasymseven}{\isamath{\mathbf{7}}} %requires amssym
9.21 +\newcommand{\isasymeight}{\isamath{\mathbf{8}}} %requires amssym
9.22 +\newcommand{\isasymnine}{\isamath{\mathbf{9}}} %requires amssym
9.23 +\newcommand{\isasymA}{\isamath{\mathcal{A}}}
9.24 +\newcommand{\isasymB}{\isamath{\mathcal{B}}}
9.25 +\newcommand{\isasymC}{\isamath{\mathcal{C}}}
9.26 +\newcommand{\isasymD}{\isamath{\mathcal{D}}}
9.27 +\newcommand{\isasymE}{\isamath{\mathcal{E}}}
9.28 +\newcommand{\isasymF}{\isamath{\mathcal{F}}}
9.29 +\newcommand{\isasymG}{\isamath{\mathcal{G}}}
9.30 +\newcommand{\isasymH}{\isamath{\mathcal{H}}}
9.31 +\newcommand{\isasymI}{\isamath{\mathcal{I}}}
9.32 +\newcommand{\isasymJ}{\isamath{\mathcal{J}}}
9.33 +\newcommand{\isasymK}{\isamath{\mathcal{K}}}
9.34 +\newcommand{\isasymL}{\isamath{\mathcal{L}}}
9.35 +\newcommand{\isasymM}{\isamath{\mathcal{M}}}
9.36 +\newcommand{\isasymN}{\isamath{\mathcal{N}}}
9.37 +\newcommand{\isasymO}{\isamath{\mathcal{O}}}
9.38 +\newcommand{\isasymP}{\isamath{\mathcal{P}}}
9.39 +\newcommand{\isasymQ}{\isamath{\mathcal{Q}}}
9.40 +\newcommand{\isasymR}{\isamath{\mathcal{R}}}
9.41 +\newcommand{\isasymS}{\isamath{\mathcal{S}}}
9.42 +\newcommand{\isasymT}{\isamath{\mathcal{T}}}
9.43 +\newcommand{\isasymU}{\isamath{\mathcal{U}}}
9.44 +\newcommand{\isasymV}{\isamath{\mathcal{V}}}
9.45 +\newcommand{\isasymW}{\isamath{\mathcal{W}}}
9.46 +\newcommand{\isasymX}{\isamath{\mathcal{X}}}
9.47 +\newcommand{\isasymY}{\isamath{\mathcal{Y}}}
9.48 +\newcommand{\isasymZ}{\isamath{\mathcal{Z}}}
9.49 +\newcommand{\isasyma}{\isamath{\mathrm{a}}}
9.50 +\newcommand{\isasymb}{\isamath{\mathrm{b}}}
9.51 +\newcommand{\isasymc}{\isamath{\mathrm{c}}}
9.52 +\newcommand{\isasymd}{\isamath{\mathrm{d}}}
9.53 +\newcommand{\isasyme}{\isamath{\mathrm{e}}}
9.54 +\newcommand{\isasymf}{\isamath{\mathrm{f}}}
9.55 +\newcommand{\isasymg}{\isamath{\mathrm{g}}}
9.56 +\newcommand{\isasymh}{\isamath{\mathrm{h}}}
9.57 +\newcommand{\isasymi}{\isamath{\mathrm{i}}}
9.58 +\newcommand{\isasymj}{\isamath{\mathrm{j}}}
9.59 +\newcommand{\isasymk}{\isamath{\mathrm{k}}}
9.60 +\newcommand{\isasyml}{\isamath{\mathrm{l}}}
9.61 +\newcommand{\isasymm}{\isamath{\mathrm{m}}}
9.62 +\newcommand{\isasymn}{\isamath{\mathrm{n}}}
9.63 +\newcommand{\isasymo}{\isamath{\mathrm{o}}}
9.64 +\newcommand{\isasymp}{\isamath{\mathrm{p}}}
9.65 +\newcommand{\isasymq}{\isamath{\mathrm{q}}}
9.66 +\newcommand{\isasymr}{\isamath{\mathrm{r}}}
9.67 +\newcommand{\isasyms}{\isamath{\mathrm{s}}}
9.68 +\newcommand{\isasymt}{\isamath{\mathrm{t}}}
9.69 +\newcommand{\isasymu}{\isamath{\mathrm{u}}}
9.70 +\newcommand{\isasymv}{\isamath{\mathrm{v}}}
9.71 +\newcommand{\isasymw}{\isamath{\mathrm{w}}}
9.72 +\newcommand{\isasymx}{\isamath{\mathrm{x}}}
9.73 +\newcommand{\isasymy}{\isamath{\mathrm{y}}}
9.74 +\newcommand{\isasymz}{\isamath{\mathrm{z}}}
9.75 +\newcommand{\isasymAA}{\isamath{\mathfrak{A}}} %requires eufrak
9.76 +\newcommand{\isasymBB}{\isamath{\mathfrak{B}}} %requires eufrak
9.77 +\newcommand{\isasymCC}{\isamath{\mathfrak{C}}} %requires eufrak
9.78 +\newcommand{\isasymDD}{\isamath{\mathfrak{D}}} %requires eufrak
9.79 +\newcommand{\isasymEE}{\isamath{\mathfrak{E}}} %requires eufrak
9.80 +\newcommand{\isasymFF}{\isamath{\mathfrak{F}}} %requires eufrak
9.81 +\newcommand{\isasymGG}{\isamath{\mathfrak{G}}} %requires eufrak
9.82 +\newcommand{\isasymHH}{\isamath{\mathfrak{H}}} %requires eufrak
9.83 +\newcommand{\isasymII}{\isamath{\mathfrak{I}}} %requires eufrak
9.84 +\newcommand{\isasymJJ}{\isamath{\mathfrak{J}}} %requires eufrak
9.85 +\newcommand{\isasymKK}{\isamath{\mathfrak{K}}} %requires eufrak
9.86 +\newcommand{\isasymLL}{\isamath{\mathfrak{L}}} %requires eufrak
9.87 +\newcommand{\isasymMM}{\isamath{\mathfrak{M}}} %requires eufrak
9.88 +\newcommand{\isasymNN}{\isamath{\mathfrak{N}}} %requires eufrak
9.89 +\newcommand{\isasymOO}{\isamath{\mathfrak{O}}} %requires eufrak
9.90 +\newcommand{\isasymPP}{\isamath{\mathfrak{P}}} %requires eufrak
9.91 +\newcommand{\isasymQQ}{\isamath{\mathfrak{Q}}} %requires eufrak
9.92 +\newcommand{\isasymRR}{\isamath{\mathfrak{R}}} %requires eufrak
9.93 +\newcommand{\isasymSS}{\isamath{\mathfrak{S}}} %requires eufrak
9.94 +\newcommand{\isasymTT}{\isamath{\mathfrak{T}}} %requires eufrak
9.95 +\newcommand{\isasymUU}{\isamath{\mathfrak{U}}} %requires eufrak
9.96 +\newcommand{\isasymVV}{\isamath{\mathfrak{V}}} %requires eufrak
9.97 +\newcommand{\isasymWW}{\isamath{\mathfrak{W}}} %requires eufrak
9.98 +\newcommand{\isasymXX}{\isamath{\mathfrak{X}}} %requires eufrak
9.99 +\newcommand{\isasymYY}{\isamath{\mathfrak{Y}}} %requires eufrak
9.100 +\newcommand{\isasymZZ}{\isamath{\mathfrak{Z}}} %requires eufrak
9.101 +\newcommand{\isasymaa}{\isamath{\mathfrak{a}}} %requires eufrak
9.102 +\newcommand{\isasymbb}{\isamath{\mathfrak{b}}} %requires eufrak
9.103 +\newcommand{\isasymcc}{\isamath{\mathfrak{c}}} %requires eufrak
9.104 +\newcommand{\isasymdd}{\isamath{\mathfrak{d}}} %requires eufrak
9.105 +\newcommand{\isasymee}{\isamath{\mathfrak{e}}} %requires eufrak
9.106 +\newcommand{\isasymff}{\isamath{\mathfrak{f}}} %requires eufrak
9.107 +\newcommand{\isasymgg}{\isamath{\mathfrak{g}}} %requires eufrak
9.108 +\newcommand{\isasymhh}{\isamath{\mathfrak{h}}} %requires eufrak
9.109 +\newcommand{\isasymii}{\isamath{\mathfrak{i}}} %requires eufrak
9.110 +\newcommand{\isasymjj}{\isamath{\mathfrak{j}}} %requires eufrak
9.111 +\newcommand{\isasymkk}{\isamath{\mathfrak{k}}} %requires eufrak
9.112 +\newcommand{\isasymll}{\isamath{\mathfrak{l}}} %requires eufrak
9.113 +\newcommand{\isasymmm}{\isamath{\mathfrak{m}}} %requires eufrak
9.114 +\newcommand{\isasymnn}{\isamath{\mathfrak{n}}} %requires eufrak
9.115 +\newcommand{\isasymoo}{\isamath{\mathfrak{o}}} %requires eufrak
9.116 +\newcommand{\isasympp}{\isamath{\mathfrak{p}}} %requires eufrak
9.117 +\newcommand{\isasymqq}{\isamath{\mathfrak{q}}} %requires eufrak
9.118 +\newcommand{\isasymrr}{\isamath{\mathfrak{r}}} %requires eufrak
9.119 +\newcommand{\isasymss}{\isamath{\mathfrak{s}}} %requires eufrak
9.120 +\newcommand{\isasymtt}{\isamath{\mathfrak{t}}} %requires eufrak
9.121 +\newcommand{\isasymuu}{\isamath{\mathfrak{u}}} %requires eufrak
9.122 +\newcommand{\isasymvv}{\isamath{\mathfrak{v}}} %requires eufrak
9.123 +\newcommand{\isasymww}{\isamath{\mathfrak{w}}} %requires eufrak
9.124 +\newcommand{\isasymxx}{\isamath{\mathfrak{x}}} %requires eufrak
9.125 +\newcommand{\isasymyy}{\isamath{\mathfrak{y}}} %requires eufrak
9.126 +\newcommand{\isasymzz}{\isamath{\mathfrak{z}}} %requires eufrak
9.127 +\newcommand{\isasymalpha}{\isamath{\alpha}}
9.128 +\newcommand{\isasymbeta}{\isamath{\beta}}
9.129 +\newcommand{\isasymgamma}{\isamath{\gamma}}
9.130 +\newcommand{\isasymdelta}{\isamath{\delta}}
9.131 +\newcommand{\isasymepsilon}{\isamath{\varepsilon}}
9.132 +\newcommand{\isasymzeta}{\isamath{\zeta}}
9.133 +\newcommand{\isasymeta}{\isamath{\eta}}
9.134 +\newcommand{\isasymtheta}{\isamath{\vartheta}}
9.135 +\newcommand{\isasymiota}{\isamath{\iota}}
9.136 +\newcommand{\isasymkappa}{\isamath{\kappa}}
9.137 +\newcommand{\isasymlambda}{\isamath{\lambda}}
9.138 +\newcommand{\isasymmu}{\isamath{\mu}}
9.139 +\newcommand{\isasymnu}{\isamath{\nu}}
9.140 +\newcommand{\isasymxi}{\isamath{\xi}}
9.141 +\newcommand{\isasympi}{\isamath{\pi}}
9.142 +\newcommand{\isasymrho}{\isamath{\varrho}}
9.143 +\newcommand{\isasymsigma}{\isamath{\sigma}}
9.144 +\newcommand{\isasymtau}{\isamath{\tau}}
9.145 +\newcommand{\isasymupsilon}{\isamath{\upsilon}}
9.146 +\newcommand{\isasymphi}{\isamath{\varphi}}
9.147 +\newcommand{\isasymchi}{\isamath{\chi}}
9.148 +\newcommand{\isasympsi}{\isamath{\psi}}
9.149 +\newcommand{\isasymomega}{\isamath{\omega}}
9.150 +\newcommand{\isasymGamma}{\isamath{\Gamma}}
9.151 +\newcommand{\isasymDelta}{\isamath{\Delta}}
9.152 +\newcommand{\isasymTheta}{\isamath{\Theta}}
9.153 +\newcommand{\isasymLambda}{\isamath{\Lambda}}
9.154 +\newcommand{\isasymXi}{\isamath{\Xi}}
9.155 +\newcommand{\isasymPi}{\isamath{\Pi}}
9.156 +\newcommand{\isasymSigma}{\isamath{\Sigma}}
9.157 +\newcommand{\isasymUpsilon}{\isamath{\Upsilon}}
9.158 +\newcommand{\isasymPhi}{\isamath{\Phi}}
9.159 +\newcommand{\isasymPsi}{\isamath{\Psi}}
9.160 +\newcommand{\isasymOmega}{\isamath{\Omega}}
9.161 +\newcommand{\isasymbool}{\isamath{\mathrm{I}\mkern-3.8mu\mathrm{B}}}
9.162 +\newcommand{\isasymcomplex}{\isamath{\mathrm{C}\mkern-15mu{\phantom{\mathrm{t}}\vrule}\mkern9mu}}
9.163 +\newcommand{\isasymnat}{\isamath{\mathrm{I}\mkern-3.8mu\mathrm{N}}}
9.164 +\newcommand{\isasymrat}{\isamath{\mathrm{Q}\mkern-16mu{\phantom{\mathrm{t}}\vrule}\mkern10mu}}
9.165 +\newcommand{\isasymreal}{\isamath{\mathrm{I}\mkern-3.8mu\mathrm{R}}}
9.166 +\newcommand{\isasymint}{\isamath{\mathsf{Z}\mkern-7.5mu\mathsf{Z}}}
9.167 +\newcommand{\isasymleftarrow}{\isamath{\leftarrow}}
9.168 +\newcommand{\isasymlongleftarrow}{\isamath{\longleftarrow}}
9.169 +\newcommand{\isasymrightarrow}{\isamath{\rightarrow}}
9.170 +\newcommand{\isasymlongrightarrow}{\isamath{\longrightarrow}}
9.171 +\newcommand{\isasymLeftarrow}{\isamath{\Leftarrow}}
9.172 +\newcommand{\isasymLongleftarrow}{\isamath{\Longleftarrow}}
9.173 +\newcommand{\isasymRightarrow}{\isamath{\Rightarrow}}
9.174 +\newcommand{\isasymLongrightarrow}{\isamath{\Longrightarrow}}
9.175 +\newcommand{\isasymleftrightarrow}{\isamath{\leftrightarrow}}
9.176 +\newcommand{\isasymlongleftrightarrow}{\isamath{\longleftrightarrow}}
9.177 +\newcommand{\isasymLeftrightarrow}{\isamath{\Leftrightarrow}}
9.178 +\newcommand{\isasymLongleftrightarrow}{\isamath{\Longleftrightarrow}}
9.179 +\newcommand{\isasymmapsto}{\isamath{\mapsto}}
9.180 +\newcommand{\isasymlongmapsto}{\isamath{\longmapsto}}
9.181 +\newcommand{\isasymmidarrow}{\isamath{\relbar}}
9.182 +\newcommand{\isasymMidarrow}{\isamath{\Relbar}}
9.183 +\newcommand{\isasymhookleftarrow}{\isamath{\hookleftarrow}}
9.184 +\newcommand{\isasymhookrightarrow}{\isamath{\hookrightarrow}}
9.185 +\newcommand{\isasymleftharpoondown}{\isamath{\leftharpoondown}}
9.186 +\newcommand{\isasymrightharpoondown}{\isamath{\rightharpoondown}}
9.187 +\newcommand{\isasymleftharpoonup}{\isamath{\leftharpoonup}}
9.188 +\newcommand{\isasymrightharpoonup}{\isamath{\rightharpoonup}}
9.189 +\newcommand{\isasymrightleftharpoons}{\isamath{\rightleftharpoons}}
9.190 +\newcommand{\isasymleadsto}{\isamath{\leadsto}} %requires amssym
9.191 +\newcommand{\isasymup}{\isamath{\uparrow}}
9.192 +\newcommand{\isasymUp}{\isamath{\Uparrow}}
9.193 +\newcommand{\isasymdown}{\isamath{\downarrow}}
9.194 +\newcommand{\isasymDown}{\isamath{\Downarrow}}
9.195 +\newcommand{\isasymupdown}{\isamath{\updownarrow}}
9.196 +\newcommand{\isasymUpdown}{\isamath{\Updownarrow}}
9.197 +\newcommand{\isasymlangle}{\isamath{\langle}}
9.198 +\newcommand{\isasymrangle}{\isamath{\rangle}}
9.199 +\newcommand{\isasymlceil}{\isamath{\lceil}}
9.200 +\newcommand{\isasymrceil}{\isamath{\rceil}}
9.201 +\newcommand{\isasymlfloor}{\isamath{\lfloor}}
9.202 +\newcommand{\isasymrfloor}{\isamath{\rfloor}}
9.203 +\newcommand{\isasymlparr}{\isamath{\mathopen{(\mkern-3mu\mid}}}
9.204 +\newcommand{\isasymrparr}{\isamath{\mathclose{\mid\mkern-3mu)}}}
9.205 +\newcommand{\isasymlbrakk}{\isamath{\mathopen{\lbrack\mkern-3mu\lbrack}}}
9.206 +\newcommand{\isasymrbrakk}{\isamath{\mathclose{\rbrack\mkern-3mu\rbrack}}}
9.207 +\newcommand{\isasymlbrace}{\isamath{\mathopen{\lbrace\mkern-4.5mu\mid}}}
9.208 +\newcommand{\isasymrbrace}{\isamath{\mathclose{\mid\mkern-4.5mu\rbrace}}}
9.209 +\newcommand{\isasymguillemotleft}{\isatext{\flqq}} %requires babel
9.210 +\newcommand{\isasymguillemotright}{\isatext{\frqq}} %requires babel
9.211 +\newcommand{\isasymColon}{\isamath{\mathrel{::}}}
9.212 +\newcommand{\isasymnot}{\isamath{\neg}}
9.213 +\newcommand{\isasymbottom}{\isamath{\bot}}
9.214 +\newcommand{\isasymtop}{\isamath{\top}}
9.215 +\newcommand{\isasymand}{\isamath{\wedge}}
9.216 +\newcommand{\isasymAnd}{\isamath{\bigwedge}}
9.217 +\newcommand{\isasymor}{\isamath{\vee}}
9.218 +\newcommand{\isasymOr}{\isamath{\bigvee}}
9.219 +\newcommand{\isasymforall}{\isamath{\forall\,}}
9.220 +\newcommand{\isasymexists}{\isamath{\exists\,}}
9.221 +\newcommand{\isasymbox}{\isamath{\Box}} %requires amssym
9.222 +\newcommand{\isasymdiamond}{\isamath{\Diamond}} %requires amssym
9.223 +\newcommand{\isasymturnstile}{\isamath{\vdash}}
9.224 +\newcommand{\isasymTurnstile}{\isamath{\models}}
9.225 +\newcommand{\isasymtturnstile}{\isamath{\vdash\!\!\!\vdash}}
9.226 +\newcommand{\isasymTTurnstile}{\isamath{\mid\!\models}}
9.227 +\newcommand{\isasymstileturn}{\isamath{\dashv}}
9.228 +\newcommand{\isasymsurd}{\isamath{\surd}}
9.229 +\newcommand{\isasymle}{\isamath{\le}}
9.230 +\newcommand{\isasymge}{\isamath{\ge}}
9.231 +\newcommand{\isasymlless}{\isamath{\ll}}
9.232 +\newcommand{\isasymggreater}{\isamath{\gg}}
9.233 +\newcommand{\isasymlesssim}{\isamath{\lesssim}} %requires amssymb
9.234 +\newcommand{\isasymgreatersim}{\isamath{\gtrsim}} %requires amssymb
9.235 +\newcommand{\isasymlessapprox}{\isamath{\lessapprox}} %requires amssymb
9.236 +\newcommand{\isasymgreaterapprox}{\isamath{\gtrapprox}} %requires amssymb
9.237 +\newcommand{\isasymin}{\isamath{\in}}
9.238 +\newcommand{\isasymnotin}{\isamath{\notin}}
9.239 +\newcommand{\isasymsubset}{\isamath{\subset}}
9.240 +\newcommand{\isasymsupset}{\isamath{\supset}}
9.241 +\newcommand{\isasymsubseteq}{\isamath{\subseteq}}
9.242 +\newcommand{\isasymsupseteq}{\isamath{\supseteq}}
9.243 +\newcommand{\isasymsqsubset}{\isamath{\sqsubset}}
9.244 +\newcommand{\isasymsqsupset}{\isamath{\sqsupset}} %requires amssym
9.245 +\newcommand{\isasymsqsubseteq}{\isamath{\sqsubseteq}}
9.246 +\newcommand{\isasymsqsupseteq}{\isamath{\sqsupseteq}}
9.247 +\newcommand{\isasyminter}{\isamath{\cap}}
9.248 +\newcommand{\isasymInter}{\isamath{\bigcap\,}}
9.249 +\newcommand{\isasymunion}{\isamath{\cup}}
9.250 +\newcommand{\isasymUnion}{\isamath{\bigcup\,}}
9.251 +\newcommand{\isasymsqunion}{\isamath{\sqcup}}
9.252 +\newcommand{\isasymSqunion}{\isamath{\bigsqcup\,}}
9.253 +\newcommand{\isasymsqinter}{\isamath{\sqcap}}
9.254 +\newcommand{\isasymSqinter}{\isamath{\bigsqcap\,}} %requires masmath
9.255 +\newcommand{\isasymuplus}{\isamath{\uplus}}
9.256 +\newcommand{\isasymUplus}{\isamath{\biguplus\,}}
9.257 +\newcommand{\isasymnoteq}{\isamath{\not=}}
9.258 +\newcommand{\isasymsim}{\isamath{\sim}}
9.259 +\newcommand{\isasymdoteq}{\isamath{\doteq}}
9.260 +\newcommand{\isasymsimeq}{\isamath{\simeq}}
9.261 +\newcommand{\isasymapprox}{\isamath{\approx}}
9.262 +\newcommand{\isasymasymp}{\isamath{\asymp}}
9.263 +\newcommand{\isasymcong}{\isamath{\cong}}
9.264 +\newcommand{\isasymsmile}{\isamath{\smile}}
9.265 +\newcommand{\isasymequiv}{\isamath{\equiv}}
9.266 +\newcommand{\isasymfrown}{\isamath{\frown}}
9.267 +\newcommand{\isasympropto}{\isamath{\propto}}
9.268 +\newcommand{\isasymbowtie}{\isamath{\bowtie}}
9.269 +\newcommand{\isasymprec}{\isamath{\prec}}
9.270 +\newcommand{\isasymsucc}{\isamath{\succ}}
9.271 +\newcommand{\isasympreceq}{\isamath{\preceq}}
9.272 +\newcommand{\isasymsucceq}{\isamath{\succeq}}
9.273 +\newcommand{\isasymparallel}{\isamath{\parallel}}
9.274 +\newcommand{\isasymbar}{\isamath{\mid}}
9.275 +\newcommand{\isasymplusminus}{\isamath{\pm}}
9.276 +\newcommand{\isasymminusplus}{\isamath{\mp}}
9.277 +\newcommand{\isasymtimes}{\isamath{\times}}
9.278 +\newcommand{\isasymdiv}{\isamath{\div}}
9.279 +\newcommand{\isasymcdot}{\isamath{\cdot}}
9.280 +\newcommand{\isasymstar}{\isamath{\star}}
9.281 +\newcommand{\isasymbullet}{\boldmath\isamath{\mathchoice{\displaystyle{\cdot}}{\textstyle{\cdot}}{\scriptstyle{\bullet}}{\scriptscriptstyle{\bullet}}}}
9.282 +\newcommand{\isasymcirc}{\isamath{\circ}}
9.283 +\newcommand{\isasymdagger}{\isamath{\dagger}}
9.284 +\newcommand{\isasymddagger}{\isamath{\ddagger}}
9.285 +\newcommand{\isasymlhd}{\isamath{\lhd}}
9.286 +\newcommand{\isasymrhd}{\isamath{\rhd}}
9.287 +\newcommand{\isasymunlhd}{\isamath{\unlhd}}
9.288 +\newcommand{\isasymunrhd}{\isamath{\unrhd}}
9.289 +\newcommand{\isasymtriangleleft}{\isamath{\triangleleft}}
9.290 +\newcommand{\isasymtriangleright}{\isamath{\triangleright}}
9.291 +\newcommand{\isasymtriangle}{\isamath{\triangle}}
9.292 +\newcommand{\isasymtriangleq}{\isamath{\triangleq}} %requires amssymb
9.293 +\newcommand{\isasymoplus}{\isamath{\oplus}}
9.294 +\newcommand{\isasymOplus}{\isamath{\bigoplus\,}}
9.295 +\newcommand{\isasymotimes}{\isamath{\otimes}}
9.296 +\newcommand{\isasymOtimes}{\isamath{\bigotimes\,}}
9.297 +\newcommand{\isasymodot}{\isamath{\odot}}
9.298 +\newcommand{\isasymOdot}{\isamath{\bigodot\,}}
9.299 +\newcommand{\isasymominus}{\isamath{\ominus}}
9.300 +\newcommand{\isasymoslash}{\isamath{\oslash}}
9.301 +\newcommand{\isasymdots}{\isamath{\dots}}
9.302 +\newcommand{\isasymcdots}{\isamath{\cdots}}
9.303 +\newcommand{\isasymSum}{\isamath{\sum\,}}
9.304 +\newcommand{\isasymProd}{\isamath{\prod\,}}
9.305 +\newcommand{\isasymCoprod}{\isamath{\coprod\,}}
9.306 +\newcommand{\isasyminfinity}{\isamath{\infty}}
9.307 +\newcommand{\isasymintegral}{\isamath{\int\,}}
9.308 +\newcommand{\isasymointegral}{\isamath{\oint\,}}
9.309 +\newcommand{\isasymclubsuit}{\isamath{\clubsuit}}
9.310 +\newcommand{\isasymdiamondsuit}{\isamath{\diamondsuit}}
9.311 +\newcommand{\isasymheartsuit}{\isamath{\heartsuit}}
9.312 +\newcommand{\isasymspadesuit}{\isamath{\spadesuit}}
9.313 +\newcommand{\isasymaleph}{\isamath{\aleph}}
9.314 +\newcommand{\isasymemptyset}{\isamath{\emptyset}}
9.315 +\newcommand{\isasymnabla}{\isamath{\nabla}}
9.316 +\newcommand{\isasympartial}{\isamath{\partial}}
9.317 +\newcommand{\isasymRe}{\isamath{\Re}}
9.318 +\newcommand{\isasymIm}{\isamath{\Im}}
9.319 +\newcommand{\isasymflat}{\isamath{\flat}}
9.320 +\newcommand{\isasymnatural}{\isamath{\natural}}
9.321 +\newcommand{\isasymsharp}{\isamath{\sharp}}
9.322 +\newcommand{\isasymangle}{\isamath{\angle}}
9.323 +\newcommand{\isasymcopyright}{\isatext{\rm\copyright}}
9.324 +\newcommand{\isasymregistered}{\isatext{\rm\textregistered}}
9.325 +\newcommand{\isasymhyphen}{\isatext{\rm-}}
9.326 +\newcommand{\isasyminverse}{\isamath{{}^{-1}}}
9.327 +\newcommand{\isasymonesuperior}{\isamath{\mathonesuperior}} %requires latin1
9.328 +\newcommand{\isasymonequarter}{\isatext{\rm\textonequarter}} %requires latin1
9.329 +\newcommand{\isasymtwosuperior}{\isamath{\mathtwosuperior}} %requires latin1
9.330 +\newcommand{\isasymonehalf}{\isatext{\rm\textonehalf}} %requires latin1
9.331 +\newcommand{\isasymthreesuperior}{\isamath{\maththreesuperior}} %requires latin1
9.332 +\newcommand{\isasymthreequarters}{\isatext{\rm\textthreequarters}} %requires latin1
9.333 +\newcommand{\isasymordfeminine}{\isatext{\rm\textordfeminine}}
9.334 +\newcommand{\isasymordmasculine}{\isatext{\rm\textordmasculine}}
9.335 +\newcommand{\isasymsection}{\isatext{\rm\S}}
9.336 +\newcommand{\isasymparagraph}{\isatext{\rm\P}}
9.337 +\newcommand{\isasymexclamdown}{\isatext{\rm\textexclamdown}}
9.338 +\newcommand{\isasymquestiondown}{\isatext{\rm\textquestiondown}}
9.339 +\newcommand{\isasymeuro}{\isatext{\textgreek{\euro}}} %requires greek babel
9.340 +\newcommand{\isasympounds}{\isamath{\pounds}}
9.341 +\newcommand{\isasymyen}{\isatext{\yen}} %requires amssymb
9.342 +\newcommand{\isasymcent}{\isatext{\textcent}} %requires textcomp
9.343 +\newcommand{\isasymcurrency}{\isatext{\textcurrency}} %requires textcomp
9.344 +\newcommand{\isasymdegree}{\isatext{\rm\textdegree}} %requires latin1
9.345 +\newcommand{\isasymamalg}{\isamath{\amalg}}
9.346 +\newcommand{\isasymmho}{\isamath{\mho}} %requires amssym
9.347 +\newcommand{\isasymlozenge}{\isamath{\lozenge}} %requires amssym
9.348 +\newcommand{\isasymJoin}{\isamath{\Join}} %requires amssym
9.349 +\newcommand{\isasymwp}{\isamath{\wp}}
9.350 +\newcommand{\isasymwrong}{\isamath{\wr}}
9.351 +\newcommand{\isasymstruct}{\isamath{\diamond}}
9.352 +\newcommand{\isasymacute}{\isatext{\'\relax}}
9.353 +\newcommand{\isasymindex}{\isatext{\i}}
9.354 +\newcommand{\isasymdieresis}{\isatext{\"\relax}}
9.355 +\newcommand{\isasymcedilla}{\isatext{\c\relax}}
9.356 +\newcommand{\isasymhungarumlaut}{\isatext{\H\relax}}
9.357 +\newcommand{\isasymspacespace}{\isamath{~~}}