--- a/src/Doc/Logics_ZF/IFOL_examples.thy Thu Jan 11 13:48:17 2018 +0100
+++ b/src/Doc/Logics_ZF/IFOL_examples.thy Fri Jan 12 14:08:53 2018 +0100
@@ -1,56 +1,56 @@
-section{*Examples of Intuitionistic Reasoning*}
+section\<open>Examples of Intuitionistic Reasoning\<close>
theory IFOL_examples imports IFOL begin
-text{*Quantifier example from the book Logic and Computation*}
+text\<open>Quantifier example from the book Logic and Computation\<close>
lemma "(EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))"
- --{* @{subgoals[display,indent=0,margin=65]} *}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
apply (rule impI)
- --{* @{subgoals[display,indent=0,margin=65]} *}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
apply (rule allI)
- --{* @{subgoals[display,indent=0,margin=65]} *}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
apply (rule exI)
- --{* @{subgoals[display,indent=0,margin=65]} *}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
apply (erule exE)
- --{* @{subgoals[display,indent=0,margin=65]} *}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
apply (erule allE)
- --{* @{subgoals[display,indent=0,margin=65]} *}
-txt{*Now @{text "apply assumption"} fails*}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
+txt\<open>Now @{text "apply assumption"} fails\<close>
oops
-text{*Trying again, with the same first two steps*}
+text\<open>Trying again, with the same first two steps\<close>
lemma "(EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))"
- --{* @{subgoals[display,indent=0,margin=65]} *}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
apply (rule impI)
- --{* @{subgoals[display,indent=0,margin=65]} *}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
apply (rule allI)
- --{* @{subgoals[display,indent=0,margin=65]} *}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
apply (erule exE)
- --{* @{subgoals[display,indent=0,margin=65]} *}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
apply (rule exI)
- --{* @{subgoals[display,indent=0,margin=65]} *}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
apply (erule allE)
- --{* @{subgoals[display,indent=0,margin=65]} *}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
apply assumption
- --{* @{subgoals[display,indent=0,margin=65]} *}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
done
lemma "(EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))"
-by (tactic {*IntPr.fast_tac @{context} 1*})
+by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
-text{*Example of Dyckhoff's method*}
+text\<open>Example of Dyckhoff's method\<close>
lemma "~ ~ ((P-->Q) | (Q-->P))"
- --{* @{subgoals[display,indent=0,margin=65]} *}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
apply (unfold not_def)
- --{* @{subgoals[display,indent=0,margin=65]} *}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
apply (rule impI)
- --{* @{subgoals[display,indent=0,margin=65]} *}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
apply (erule disj_impE)
- --{* @{subgoals[display,indent=0,margin=65]} *}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
apply (erule imp_impE)
- --{* @{subgoals[display,indent=0,margin=65]} *}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
apply (erule imp_impE)
- --{* @{subgoals[display,indent=0,margin=65]} *}
+ \<comment>\<open>@{subgoals[display,indent=0,margin=65]}\<close>
apply assumption
apply (erule FalseE)+
done