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src/Cube/Example.thy
changeset 36319 8feb2c4bef1a
parent 35762 af3ff2ba4c54
child 42814 5af15f1e2ef6 
--- a/src/Cube/Example.thy	Fri Apr 23 23:33:48 2010 +0200
+++ b/src/Cube/Example.thy	Fri Apr 23 23:35:43 2010 +0200
@@ -30,98 +30,98 @@
 
 subsection {* Simple types *}
 
-lemma "A:* |- A->A : ?T"
+schematic_lemma "A:* |- A->A : ?T"
   by (depth_solve rules)
 
-lemma "A:* |- Lam a:A. a : ?T"
+schematic_lemma "A:* |- Lam a:A. a : ?T"
   by (depth_solve rules)
 
-lemma "A:* B:* b:B |- Lam x:A. b : ?T"
+schematic_lemma "A:* B:* b:B |- Lam x:A. b : ?T"
   by (depth_solve rules)
 
-lemma "A:* b:A |- (Lam a:A. a)^b: ?T"
+schematic_lemma "A:* b:A |- (Lam a:A. a)^b: ?T"
   by (depth_solve rules)
 
-lemma "A:* B:* c:A b:B |- (Lam x:A. b)^ c: ?T"
+schematic_lemma "A:* B:* c:A b:B |- (Lam x:A. b)^ c: ?T"
   by (depth_solve rules)
 
-lemma "A:* B:* |- Lam a:A. Lam b:B. a : ?T"
+schematic_lemma "A:* B:* |- Lam a:A. Lam b:B. a : ?T"
   by (depth_solve rules)
 
 
 subsection {* Second-order types *}
 
-lemma (in L2) "|- Lam A:*. Lam a:A. a : ?T"
+schematic_lemma (in L2) "|- Lam A:*. Lam a:A. a : ?T"
   by (depth_solve rules)
 
-lemma (in L2) "A:* |- (Lam B:*.Lam b:B. b)^A : ?T"
+schematic_lemma (in L2) "A:* |- (Lam B:*.Lam b:B. b)^A : ?T"
   by (depth_solve rules)
 
-lemma (in L2) "A:* b:A |- (Lam B:*.Lam b:B. b) ^ A ^ b: ?T"
+schematic_lemma (in L2) "A:* b:A |- (Lam B:*.Lam b:B. b) ^ A ^ b: ?T"
   by (depth_solve rules)
 
-lemma (in L2) "|- Lam B:*.Lam a:(Pi A:*.A).a ^ ((Pi A:*.A)->B) ^ a: ?T"
+schematic_lemma (in L2) "|- Lam B:*.Lam a:(Pi A:*.A).a ^ ((Pi A:*.A)->B) ^ a: ?T"
   by (depth_solve rules)
 
 
 subsection {* Weakly higher-order propositional logic *}
 
-lemma (in Lomega) "|- Lam A:*.A->A : ?T"
+schematic_lemma (in Lomega) "|- Lam A:*.A->A : ?T"
   by (depth_solve rules)
 
-lemma (in Lomega) "B:* |- (Lam A:*.A->A) ^ B : ?T"
+schematic_lemma (in Lomega) "B:* |- (Lam A:*.A->A) ^ B : ?T"
   by (depth_solve rules)
 
-lemma (in Lomega) "B:* b:B |- (Lam y:B. b): ?T"
+schematic_lemma (in Lomega) "B:* b:B |- (Lam y:B. b): ?T"
   by (depth_solve rules)
 
-lemma (in Lomega) "A:* F:*->* |- F^(F^A): ?T"
+schematic_lemma (in Lomega) "A:* F:*->* |- F^(F^A): ?T"
   by (depth_solve rules)
 
-lemma (in Lomega) "A:* |- Lam F:*->*.F^(F^A): ?T"
+schematic_lemma (in Lomega) "A:* |- Lam F:*->*.F^(F^A): ?T"
   by (depth_solve rules)
 
 
 subsection {* LP *}
 
-lemma (in LP) "A:* |- A -> * : ?T"
+schematic_lemma (in LP) "A:* |- A -> * : ?T"
   by (depth_solve rules)
 
-lemma (in LP) "A:* P:A->* a:A |- P^a: ?T"
+schematic_lemma (in LP) "A:* P:A->* a:A |- P^a: ?T"
   by (depth_solve rules)
 
-lemma (in LP) "A:* P:A->A->* a:A |- Pi a:A. P^a^a: ?T"
+schematic_lemma (in LP) "A:* P:A->A->* a:A |- Pi a:A. P^a^a: ?T"
   by (depth_solve rules)
 
-lemma (in LP) "A:* P:A->* Q:A->* |- Pi a:A. P^a -> Q^a: ?T"
+schematic_lemma (in LP) "A:* P:A->* Q:A->* |- Pi a:A. P^a -> Q^a: ?T"
   by (depth_solve rules)
 
-lemma (in LP) "A:* P:A->* |- Pi a:A. P^a -> P^a: ?T"
+schematic_lemma (in LP) "A:* P:A->* |- Pi a:A. P^a -> P^a: ?T"
   by (depth_solve rules)
 
-lemma (in LP) "A:* P:A->* |- Lam a:A. Lam x:P^a. x: ?T"
+schematic_lemma (in LP) "A:* P:A->* |- Lam a:A. Lam x:P^a. x: ?T"
   by (depth_solve rules)
 
-lemma (in LP) "A:* P:A->* Q:* |- (Pi a:A. P^a->Q) -> (Pi a:A. P^a) -> Q : ?T"
+schematic_lemma (in LP) "A:* P:A->* Q:* |- (Pi a:A. P^a->Q) -> (Pi a:A. P^a) -> Q : ?T"
   by (depth_solve rules)
 
-lemma (in LP) "A:* P:A->* Q:* a0:A |-
+schematic_lemma (in LP) "A:* P:A->* Q:* a0:A |-
         Lam x:Pi a:A. P^a->Q. Lam y:Pi a:A. P^a. x^a0^(y^a0): ?T"
   by (depth_solve rules)
 
 
 subsection {* Omega-order types *}
 
-lemma (in L2) "A:* B:* |- Pi C:*.(A->B->C)->C : ?T"
+schematic_lemma (in L2) "A:* B:* |- Pi C:*.(A->B->C)->C : ?T"
   by (depth_solve rules)
 
-lemma (in Lomega2) "|- Lam A:*.Lam B:*.Pi C:*.(A->B->C)->C : ?T"
+schematic_lemma (in Lomega2) "|- Lam A:*.Lam B:*.Pi C:*.(A->B->C)->C : ?T"
   by (depth_solve rules)
 
-lemma (in Lomega2) "|- Lam A:*.Lam B:*.Lam x:A. Lam y:B. x : ?T"
+schematic_lemma (in Lomega2) "|- Lam A:*.Lam B:*.Lam x:A. Lam y:B. x : ?T"
   by (depth_solve rules)
 
-lemma (in Lomega2) "A:* B:* |- ?p : (A->B) -> ((B->Pi P:*.P)->(A->Pi P:*.P))"
+schematic_lemma (in Lomega2) "A:* B:* |- ?p : (A->B) -> ((B->Pi P:*.P)->(A->Pi P:*.P))"
   apply (strip_asms rules)
   apply (rule lam_ss)
     apply (depth_solve1 rules)
@@ -145,14 +145,14 @@
 
 subsection {* Second-order Predicate Logic *}
 
-lemma (in LP2) "A:* P:A->* |- Lam a:A. P^a->(Pi A:*.A) : ?T"
+schematic_lemma (in LP2) "A:* P:A->* |- Lam a:A. P^a->(Pi A:*.A) : ?T"
   by (depth_solve rules)
 
-lemma (in LP2) "A:* P:A->A->* |-
+schematic_lemma (in LP2) "A:* P:A->A->* |-
     (Pi a:A. Pi b:A. P^a^b->P^b^a->Pi P:*.P) -> Pi a:A. P^a^a->Pi P:*.P : ?T"
   by (depth_solve rules)
 
-lemma (in LP2) "A:* P:A->A->* |-
+schematic_lemma (in LP2) "A:* P:A->A->* |-
     ?p: (Pi a:A. Pi b:A. P^a^b->P^b^a->Pi P:*.P) -> Pi a:A. P^a^a->Pi P:*.P"
   -- {* Antisymmetry implies irreflexivity: *}
   apply (strip_asms rules)
@@ -174,22 +174,22 @@
 
 subsection {* LPomega *}
 
-lemma (in LPomega) "A:* |- Lam P:A->A->*.Lam a:A. P^a^a : ?T"
+schematic_lemma (in LPomega) "A:* |- Lam P:A->A->*.Lam a:A. P^a^a : ?T"
   by (depth_solve rules)
 
-lemma (in LPomega) "|- Lam A:*.Lam P:A->A->*.Lam a:A. P^a^a : ?T"
+schematic_lemma (in LPomega) "|- Lam A:*.Lam P:A->A->*.Lam a:A. P^a^a : ?T"
   by (depth_solve rules)
 
 
 subsection {* Constructions *}
 
-lemma (in CC) "|- Lam A:*.Lam P:A->*.Lam a:A. P^a->Pi P:*.P: ?T"
+schematic_lemma (in CC) "|- Lam A:*.Lam P:A->*.Lam a:A. P^a->Pi P:*.P: ?T"
   by (depth_solve rules)
 
-lemma (in CC) "|- Lam A:*.Lam P:A->*.Pi a:A. P^a: ?T"
+schematic_lemma (in CC) "|- Lam A:*.Lam P:A->*.Pi a:A. P^a: ?T"
   by (depth_solve rules)
 
-lemma (in CC) "A:* P:A->* a:A |- ?p : (Pi a:A. P^a)->P^a"
+schematic_lemma (in CC) "A:* P:A->* a:A |- ?p : (Pi a:A. P^a)->P^a"
   apply (strip_asms rules)
   apply (rule lam_ss)
     apply (depth_solve1 rules)
@@ -201,15 +201,15 @@
 
 subsection {* Some random examples *}
 
-lemma (in LP2) "A:* c:A f:A->A |-
+schematic_lemma (in LP2) "A:* c:A f:A->A |-
     Lam a:A. Pi P:A->*.P^c -> (Pi x:A. P^x->P^(f^x)) -> P^a : ?T"
   by (depth_solve rules)
 
-lemma (in CC) "Lam A:*.Lam c:A. Lam f:A->A.
+schematic_lemma (in CC) "Lam A:*.Lam c:A. Lam f:A->A.
     Lam a:A. Pi P:A->*.P^c -> (Pi x:A. P^x->P^(f^x)) -> P^a : ?T"
   by (depth_solve rules)
 
-lemma (in LP2)
+schematic_lemma (in LP2)
   "A:* a:A b:A |- ?p: (Pi P:A->*.P^a->P^b) -> (Pi P:A->*.P^b->P^a)"
   -- {* Symmetry of Leibnitz equality *}
   apply (strip_asms rules)
isabelle