src/FOLP/ex/Propositional_Int.thy

--- a/src/FOLP/ex/Propositional_Int.thy	Thu Jul 23 14:20:51 2015 +0200
+++ b/src/FOLP/ex/Propositional_Int.thy	Thu Jul 23 14:25:05 2015 +0200
@@ -3,7 +3,7 @@
     Copyright   1991  University of Cambridge
 *)
 
-section {* First-Order Logic: propositional examples *}
+section \<open>First-Order Logic: propositional examples\<close>
 
 theory Propositional_Int
 imports IFOLP
@@ -12,106 +12,106 @@
 
 text "commutative laws of & and | "
 schematic_lemma "?p : P & Q  -->  Q & P"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 schematic_lemma "?p : P | Q  -->  Q | P"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 
 text "associative laws of & and | "
 schematic_lemma "?p : (P & Q) & R  -->  P & (Q & R)"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 schematic_lemma "?p : (P | Q) | R  -->  P | (Q | R)"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 
 text "distributive laws of & and | "
 schematic_lemma "?p : (P & Q) | R  --> (P | R) & (Q | R)"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 schematic_lemma "?p : (P | R) & (Q | R)  --> (P & Q) | R"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 schematic_lemma "?p : (P | Q) & R  --> (P & R) | (Q & R)"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 
 schematic_lemma "?p : (P & R) | (Q & R)  --> (P | Q) & R"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 
 text "Laws involving implication"
 
 schematic_lemma "?p : (P-->R) & (Q-->R) <-> (P|Q --> R)"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 schematic_lemma "?p : (P & Q --> R) <-> (P--> (Q-->R))"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 schematic_lemma "?p : ((P-->R)-->R) --> ((Q-->R)-->R) --> (P&Q-->R) --> R"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 schematic_lemma "?p : ~(P-->R) --> ~(Q-->R) --> ~(P&Q-->R)"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 schematic_lemma "?p : (P --> Q & R) <-> (P-->Q)  &  (P-->R)"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 
 text "Propositions-as-types"
 
 (*The combinator K*)
 schematic_lemma "?p : P --> (Q --> P)"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 (*The combinator S*)
 schematic_lemma "?p : (P-->Q-->R)  --> (P-->Q) --> (P-->R)"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 
 (*Converse is classical*)
 schematic_lemma "?p : (P-->Q) | (P-->R)  -->  (P --> Q | R)"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 schematic_lemma "?p : (P-->Q)  -->  (~Q --> ~P)"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 
 text "Schwichtenberg's examples (via T. Nipkow)"
 
 schematic_lemma stab_imp: "?p : (((Q-->R)-->R)-->Q) --> (((P-->Q)-->R)-->R)-->P-->Q"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 schematic_lemma stab_to_peirce: "?p : (((P --> R) --> R) --> P) --> (((Q --> R) --> R) --> Q)  
               --> ((P --> Q) --> P) --> P"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 schematic_lemma peirce_imp1: "?p : (((Q --> R) --> Q) --> Q)  
                --> (((P --> Q) --> R) --> P --> Q) --> P --> Q"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
   
 schematic_lemma peirce_imp2: "?p : (((P --> R) --> P) --> P) --> ((P --> Q --> R) --> P) --> P"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 schematic_lemma mints: "?p : ((((P --> Q) --> P) --> P) --> Q) --> Q"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 schematic_lemma mints_solovev: "?p : (P --> (Q --> R) --> Q) --> ((P --> Q) --> R) --> R"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 schematic_lemma tatsuta: "?p : (((P7 --> P1) --> P10) --> P4 --> P5)  
           --> (((P8 --> P2) --> P9) --> P3 --> P10)  
           --> (P1 --> P8) --> P6 --> P7  
           --> (((P3 --> P2) --> P9) --> P4)  
           --> (P1 --> P3) --> (((P6 --> P1) --> P2) --> P9) --> P5"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 schematic_lemma tatsuta1: "?p : (((P8 --> P2) --> P9) --> P3 --> P10)  
      --> (((P3 --> P2) --> P9) --> P4)  
      --> (((P6 --> P1) --> P2) --> P9)  
      --> (((P7 --> P1) --> P10) --> P4 --> P5)  
      --> (P1 --> P3) --> (P1 --> P8) --> P6 --> P7 --> P5"
-  by (tactic {* IntPr.fast_tac @{context} 1 *})
+  by (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
 
 end