
diff -r e15f053a42d8 -r e65314985426 src/FOL/ex/Propositional_Int.thy
--- a/src/FOL/ex/Propositional_Int.thy	Thu Jan 03 21:48:05 2019 +0100
+++ b/src/FOL/ex/Propositional_Int.thy	Thu Jan 03 22:19:19 2019 +0100
@@ -11,110 +11,110 @@
 
 text \<open>commutative laws of \<open>\<and>\<close> and \<open>\<or>\<close>\<close>
 
-lemma "P \<and> Q \<longrightarrow> Q \<and> P"
+lemma \<open>P \<and> Q \<longrightarrow> Q \<and> P\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
-lemma "P \<or> Q \<longrightarrow> Q \<or> P"
+lemma \<open>P \<or> Q \<longrightarrow> Q \<or> P\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
 
 text \<open>associative laws of \<open>\<and>\<close> and \<open>\<or>\<close>\<close>
-lemma "(P \<and> Q) \<and> R \<longrightarrow> P \<and> (Q \<and> R)"
+lemma \<open>(P \<and> Q) \<and> R \<longrightarrow> P \<and> (Q \<and> R)\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
-lemma "(P \<or> Q) \<or> R \<longrightarrow> P \<or> (Q \<or> R)"
+lemma \<open>(P \<or> Q) \<or> R \<longrightarrow> P \<or> (Q \<or> R)\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
 
 text \<open>distributive laws of \<open>\<and>\<close> and \<open>\<or>\<close>\<close>
-lemma "(P \<and> Q) \<or> R \<longrightarrow> (P \<or> R) \<and> (Q \<or> R)"
+lemma \<open>(P \<and> Q) \<or> R \<longrightarrow> (P \<or> R) \<and> (Q \<or> R)\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
-lemma "(P \<or> R) \<and> (Q \<or> R) \<longrightarrow> (P \<and> Q) \<or> R"
+lemma \<open>(P \<or> R) \<and> (Q \<or> R) \<longrightarrow> (P \<and> Q) \<or> R\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
-lemma "(P \<or> Q) \<and> R \<longrightarrow> (P \<and> R) \<or> (Q \<and> R)"
+lemma \<open>(P \<or> Q) \<and> R \<longrightarrow> (P \<and> R) \<or> (Q \<and> R)\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
-lemma "(P \<and> R) \<or> (Q \<and> R) \<longrightarrow> (P \<or> Q) \<and> R"
+lemma \<open>(P \<and> R) \<or> (Q \<and> R) \<longrightarrow> (P \<or> Q) \<and> R\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
 
 text \<open>Laws involving implication\<close>
 
-lemma "(P \<longrightarrow> R) \<and> (Q \<longrightarrow> R) \<longleftrightarrow> (P \<or> Q \<longrightarrow> R)"
+lemma \<open>(P \<longrightarrow> R) \<and> (Q \<longrightarrow> R) \<longleftrightarrow> (P \<or> Q \<longrightarrow> R)\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
-lemma "(P \<and> Q \<longrightarrow> R) \<longleftrightarrow> (P \<longrightarrow> (Q \<longrightarrow> R))"
+lemma \<open>(P \<and> Q \<longrightarrow> R) \<longleftrightarrow> (P \<longrightarrow> (Q \<longrightarrow> R))\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
-lemma "((P \<longrightarrow> R) \<longrightarrow> R) \<longrightarrow> ((Q \<longrightarrow> R) \<longrightarrow> R) \<longrightarrow> (P \<and> Q \<longrightarrow> R) \<longrightarrow> R"
+lemma \<open>((P \<longrightarrow> R) \<longrightarrow> R) \<longrightarrow> ((Q \<longrightarrow> R) \<longrightarrow> R) \<longrightarrow> (P \<and> Q \<longrightarrow> R) \<longrightarrow> R\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
-lemma "\<not> (P \<longrightarrow> R) \<longrightarrow> \<not> (Q \<longrightarrow> R) \<longrightarrow> \<not> (P \<and> Q \<longrightarrow> R)"
+lemma \<open>\<not> (P \<longrightarrow> R) \<longrightarrow> \<not> (Q \<longrightarrow> R) \<longrightarrow> \<not> (P \<and> Q \<longrightarrow> R)\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
-lemma "(P \<longrightarrow> Q \<and> R) \<longleftrightarrow> (P \<longrightarrow> Q) \<and> (P \<longrightarrow> R)"
+lemma \<open>(P \<longrightarrow> Q \<and> R) \<longleftrightarrow> (P \<longrightarrow> Q) \<and> (P \<longrightarrow> R)\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
 
 text \<open>Propositions-as-types\<close>
 
 \<comment> \<open>The combinator K\<close>
-lemma "P \<longrightarrow> (Q \<longrightarrow> P)"
+lemma \<open>P \<longrightarrow> (Q \<longrightarrow> P)\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
 \<comment> \<open>The combinator S\<close>
-lemma "(P \<longrightarrow> Q \<longrightarrow> R) \<longrightarrow> (P \<longrightarrow> Q) \<longrightarrow> (P \<longrightarrow> R)"
+lemma \<open>(P \<longrightarrow> Q \<longrightarrow> R) \<longrightarrow> (P \<longrightarrow> Q) \<longrightarrow> (P \<longrightarrow> R)\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
 
 \<comment> \<open>Converse is classical\<close>
-lemma "(P \<longrightarrow> Q) \<or> (P \<longrightarrow> R) \<longrightarrow> (P \<longrightarrow> Q \<or> R)"
+lemma \<open>(P \<longrightarrow> Q) \<or> (P \<longrightarrow> R) \<longrightarrow> (P \<longrightarrow> Q \<or> R)\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
-lemma "(P \<longrightarrow> Q) \<longrightarrow> (\<not> Q \<longrightarrow> \<not> P)"
+lemma \<open>(P \<longrightarrow> Q) \<longrightarrow> (\<not> Q \<longrightarrow> \<not> P)\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
 
 text \<open>Schwichtenberg's examples (via T. Nipkow)\<close>
 
-lemma stab_imp: "(((Q \<longrightarrow> R) \<longrightarrow> R) \<longrightarrow> Q) \<longrightarrow> (((P \<longrightarrow> Q) \<longrightarrow> R) \<longrightarrow> R) \<longrightarrow> P \<longrightarrow> Q"
+lemma stab_imp: \<open>(((Q \<longrightarrow> R) \<longrightarrow> R) \<longrightarrow> Q) \<longrightarrow> (((P \<longrightarrow> Q) \<longrightarrow> R) \<longrightarrow> R) \<longrightarrow> P \<longrightarrow> Q\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
 lemma stab_to_peirce:
-  "(((P \<longrightarrow> R) \<longrightarrow> R) \<longrightarrow> P) \<longrightarrow> (((Q \<longrightarrow> R) \<longrightarrow> R) \<longrightarrow> Q)
-    \<longrightarrow> ((P \<longrightarrow> Q) \<longrightarrow> P) \<longrightarrow> P"
+  \<open>(((P \<longrightarrow> R) \<longrightarrow> R) \<longrightarrow> P) \<longrightarrow> (((Q \<longrightarrow> R) \<longrightarrow> R) \<longrightarrow> Q)
+    \<longrightarrow> ((P \<longrightarrow> Q) \<longrightarrow> P) \<longrightarrow> P\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
 lemma peirce_imp1:
-  "(((Q \<longrightarrow> R) \<longrightarrow> Q) \<longrightarrow> Q)
-    \<longrightarrow> (((P \<longrightarrow> Q) \<longrightarrow> R) \<longrightarrow> P \<longrightarrow> Q) \<longrightarrow> P \<longrightarrow> Q"
+  \<open>(((Q \<longrightarrow> R) \<longrightarrow> Q) \<longrightarrow> Q)
+    \<longrightarrow> (((P \<longrightarrow> Q) \<longrightarrow> R) \<longrightarrow> P \<longrightarrow> Q) \<longrightarrow> P \<longrightarrow> Q\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
-lemma peirce_imp2: "(((P \<longrightarrow> R) \<longrightarrow> P) \<longrightarrow> P) \<longrightarrow> ((P \<longrightarrow> Q \<longrightarrow> R) \<longrightarrow> P) \<longrightarrow> P"
+lemma peirce_imp2: \<open>(((P \<longrightarrow> R) \<longrightarrow> P) \<longrightarrow> P) \<longrightarrow> ((P \<longrightarrow> Q \<longrightarrow> R) \<longrightarrow> P) \<longrightarrow> P\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
-lemma mints: "((((P \<longrightarrow> Q) \<longrightarrow> P) \<longrightarrow> P) \<longrightarrow> Q) \<longrightarrow> Q"
+lemma mints: \<open>((((P \<longrightarrow> Q) \<longrightarrow> P) \<longrightarrow> P) \<longrightarrow> Q) \<longrightarrow> Q\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
-lemma mints_solovev: "(P \<longrightarrow> (Q \<longrightarrow> R) \<longrightarrow> Q) \<longrightarrow> ((P \<longrightarrow> Q) \<longrightarrow> R) \<longrightarrow> R"
+lemma mints_solovev: \<open>(P \<longrightarrow> (Q \<longrightarrow> R) \<longrightarrow> Q) \<longrightarrow> ((P \<longrightarrow> Q) \<longrightarrow> R) \<longrightarrow> R\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
 lemma tatsuta:
-  "(((P7 \<longrightarrow> P1) \<longrightarrow> P10) \<longrightarrow> P4 \<longrightarrow> P5)
+  \<open>(((P7 \<longrightarrow> P1) \<longrightarrow> P10) \<longrightarrow> P4 \<longrightarrow> P5)
   \<longrightarrow> (((P8 \<longrightarrow> P2) \<longrightarrow> P9) \<longrightarrow> P3 \<longrightarrow> P10)
   \<longrightarrow> (P1 \<longrightarrow> P8) \<longrightarrow> P6 \<longrightarrow> P7
   \<longrightarrow> (((P3 \<longrightarrow> P2) \<longrightarrow> P9) \<longrightarrow> P4)
-  \<longrightarrow> (P1 \<longrightarrow> P3) \<longrightarrow> (((P6 \<longrightarrow> P1) \<longrightarrow> P2) \<longrightarrow> P9) \<longrightarrow> P5"
+  \<longrightarrow> (P1 \<longrightarrow> P3) \<longrightarrow> (((P6 \<longrightarrow> P1) \<longrightarrow> P2) \<longrightarrow> P9) \<longrightarrow> P5\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
 lemma tatsuta1:
-  "(((P8 \<longrightarrow> P2) \<longrightarrow> P9) \<longrightarrow> P3 \<longrightarrow> P10)
+  \<open>(((P8 \<longrightarrow> P2) \<longrightarrow> P9) \<longrightarrow> P3 \<longrightarrow> P10)
   \<longrightarrow> (((P3 \<longrightarrow> P2) \<longrightarrow> P9) \<longrightarrow> P4)
   \<longrightarrow> (((P6 \<longrightarrow> P1) \<longrightarrow> P2) \<longrightarrow> P9)
   \<longrightarrow> (((P7 \<longrightarrow> P1) \<longrightarrow> P10) \<longrightarrow> P4 \<longrightarrow> P5)
-  \<longrightarrow> (P1 \<longrightarrow> P3) \<longrightarrow> (P1 \<longrightarrow> P8) \<longrightarrow> P6 \<longrightarrow> P7 \<longrightarrow> P5"
+  \<longrightarrow> (P1 \<longrightarrow> P3) \<longrightarrow> (P1 \<longrightarrow> P8) \<longrightarrow> P6 \<longrightarrow> P7 \<longrightarrow> P5\<close>
   by (tactic "IntPr.fast_tac @{context} 1")
 
 end




