--- a/src/FOLP/ex/Quantifiers_Cla.thy Tue Oct 06 13:31:44 2015 +0200
+++ b/src/FOLP/ex/Quantifiers_Cla.thy Tue Oct 06 15:14:28 2015 +0200
@@ -10,92 +10,92 @@
imports FOLP
begin
-schematic_lemma "?p : (ALL x y. P(x,y)) --> (ALL y x. P(x,y))"
+schematic_goal "?p : (ALL x y. P(x,y)) --> (ALL y x. P(x,y))"
by (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)
-schematic_lemma "?p : (EX x y. P(x,y)) --> (EX y x. P(x,y))"
+schematic_goal "?p : (EX x y. P(x,y)) --> (EX y x. P(x,y))"
by (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)
(*Converse is false*)
-schematic_lemma "?p : (ALL x. P(x)) | (ALL x. Q(x)) --> (ALL x. P(x) | Q(x))"
+schematic_goal "?p : (ALL x. P(x)) | (ALL x. Q(x)) --> (ALL x. P(x) | Q(x))"
by (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)
-schematic_lemma "?p : (ALL x. P-->Q(x)) <-> (P--> (ALL x. Q(x)))"
+schematic_goal "?p : (ALL x. P-->Q(x)) <-> (P--> (ALL x. Q(x)))"
by (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)
-schematic_lemma "?p : (ALL x. P(x)-->Q) <-> ((EX x. P(x)) --> Q)"
+schematic_goal "?p : (ALL x. P(x)-->Q) <-> ((EX x. P(x)) --> Q)"
by (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)
text "Some harder ones"
-schematic_lemma "?p : (EX x. P(x) | Q(x)) <-> (EX x. P(x)) | (EX x. Q(x))"
+schematic_goal "?p : (EX x. P(x) | Q(x)) <-> (EX x. P(x)) | (EX x. Q(x))"
by (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)
(*Converse is false*)
-schematic_lemma "?p : (EX x. P(x)&Q(x)) --> (EX x. P(x)) & (EX x. Q(x))"
+schematic_goal "?p : (EX x. P(x)&Q(x)) --> (EX x. P(x)) & (EX x. Q(x))"
by (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)
text "Basic test of quantifier reasoning"
(*TRUE*)
-schematic_lemma "?p : (EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))"
+schematic_goal "?p : (EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))"
by (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)
-schematic_lemma "?p : (ALL x. Q(x)) --> (EX x. Q(x))"
+schematic_goal "?p : (ALL x. Q(x)) --> (EX x. Q(x))"
by (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)
text "The following should fail, as they are false!"
-schematic_lemma "?p : (ALL x. EX y. Q(x,y)) --> (EX y. ALL x. Q(x,y))"
+schematic_goal "?p : (ALL x. EX y. Q(x,y)) --> (EX y. ALL x. Q(x,y))"
apply (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)?
oops
-schematic_lemma "?p : (EX x. Q(x)) --> (ALL x. Q(x))"
+schematic_goal "?p : (EX x. Q(x)) --> (ALL x. Q(x))"
apply (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)?
oops
-schematic_lemma "?p : P(?a) --> (ALL x. P(x))"
+schematic_goal "?p : P(?a) --> (ALL x. P(x))"
apply (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)?
oops
-schematic_lemma "?p : (P(?a) --> (ALL x. Q(x))) --> (ALL x. P(x) --> Q(x))"
+schematic_goal "?p : (P(?a) --> (ALL x. Q(x))) --> (ALL x. P(x) --> Q(x))"
apply (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)?
oops
text "Back to things that are provable..."
-schematic_lemma "?p : (ALL x. P(x)-->Q(x)) & (EX x. P(x)) --> (EX x. Q(x))"
+schematic_goal "?p : (ALL x. P(x)-->Q(x)) & (EX x. P(x)) --> (EX x. Q(x))"
by (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)
(*An example of why exI should be delayed as long as possible*)
-schematic_lemma "?p : (P --> (EX x. Q(x))) & P --> (EX x. Q(x))"
+schematic_goal "?p : (P --> (EX x. Q(x))) & P --> (EX x. Q(x))"
by (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)
-schematic_lemma "?p : (ALL x. P(x)-->Q(f(x))) & (ALL x. Q(x)-->R(g(x))) & P(d) --> R(?a)"
+schematic_goal "?p : (ALL x. P(x)-->Q(f(x))) & (ALL x. Q(x)-->R(g(x))) & P(d) --> R(?a)"
by (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)
-schematic_lemma "?p : (ALL x. Q(x)) --> (EX x. Q(x))"
+schematic_goal "?p : (ALL x. Q(x)) --> (EX x. Q(x))"
by (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)
text "Some slow ones"
(*Principia Mathematica *11.53 *)
-schematic_lemma "?p : (ALL x y. P(x) --> Q(y)) <-> ((EX x. P(x)) --> (ALL y. Q(y)))"
+schematic_goal "?p : (ALL x y. P(x) --> Q(y)) <-> ((EX x. P(x)) --> (ALL y. Q(y)))"
by (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)
(*Principia Mathematica *11.55 *)
-schematic_lemma "?p : (EX x y. P(x) & Q(x,y)) <-> (EX x. P(x) & (EX y. Q(x,y)))"
+schematic_goal "?p : (EX x y. P(x) & Q(x,y)) <-> (EX x. P(x) & (EX y. Q(x,y)))"
by (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)
(*Principia Mathematica *11.61 *)
-schematic_lemma "?p : (EX y. ALL x. P(x) --> Q(x,y)) --> (ALL x. P(x) --> (EX y. Q(x,y)))"
+schematic_goal "?p : (EX y. ALL x. P(x) --> Q(x,y)) --> (ALL x. P(x) --> (EX y. Q(x,y)))"
by (tactic \<open>Cla.fast_tac @{context} FOLP_cs 1\<close>)
end