1 header{*Examples of Classical Reasoning*}
3 theory FOL_examples imports FOL begin
5 lemma "EX y. ALL x. P(y)-->P(x)"
6 --{* @{subgoals[display,indent=0,margin=65]} *}
8 --{* @{subgoals[display,indent=0,margin=65]} *}
10 --{* @{subgoals[display,indent=0,margin=65]} *}
12 --{* @{subgoals[display,indent=0,margin=65]} *}
14 --{* @{subgoals[display,indent=0,margin=65]} *}
15 txt{*see below for @{text allI} combined with @{text swap}*}
16 apply (erule allI [THEN [2] swap])
17 --{* @{subgoals[display,indent=0,margin=65]} *}
19 --{* @{subgoals[display,indent=0,margin=65]} *}
21 --{* @{subgoals[display,indent=0,margin=65]} *}
26 @{thm[display] allI [THEN [2] swap]}
29 lemma "EX y. ALL x. P(y)-->P(x)"