X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1%2Fwf3%2Fprops.ma;h=aec1f02ef99e2c6892d08fc70697b6e6ce42ca75;hb=57ae1762497a5f3ea75740e2908e04adb8642cc2;hp=98a05c6378bbd46baa2bc1906d30b1148886dd09;hpb=88a68a9c334646bc17314d5327cd3b790202acd6;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_1/wf3/props.ma b/matita/matita/contribs/lambdadelta/basic_1/wf3/props.ma
index 98a05c637..aec1f02ef 100644
--- a/matita/matita/contribs/lambdadelta/basic_1/wf3/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/wf3/props.ma
@@ -14,91 +14,11 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/wf3/ty3.ma".
+include "basic_1/wf3/ty3.ma".
 
-include "Basic-1/app/defs.ma".
+include "basic_1/app/defs.ma".
 
-theorem wf3_mono:
- \forall (g: G).(\forall (c: C).(\forall (c1: C).((wf3 g c c1) \to (\forall 
-(c2: C).((wf3 g c c2) \to (eq C c1 c2))))))
-\def
- \lambda (g: G).(\lambda (c: C).(\lambda (c1: C).(\lambda (H: (wf3 g c 
-c1)).(wf3_ind g (\lambda (c0: C).(\lambda (c2: C).(\forall (c3: C).((wf3 g c0 
-c3) \to (eq C c2 c3))))) (\lambda (m: nat).(\lambda (c2: C).(\lambda (H0: 
-(wf3 g (CSort m) c2)).(let H_y \def (wf3_gen_sort1 g c2 m H0) in (eq_ind_r C 
-(CSort m) (\lambda (c0: C).(eq C (CSort m) c0)) (refl_equal C (CSort m)) c2 
-H_y))))) (\lambda (c2: C).(\lambda (c3: C).(\lambda (_: (wf3 g c2 
-c3)).(\lambda (H1: ((\forall (c4: C).((wf3 g c2 c4) \to (eq C c3 
-c4))))).(\lambda (u: T).(\lambda (t: T).(\lambda (H2: (ty3 g c2 u 
-t)).(\lambda (b: B).(\lambda (c0: C).(\lambda (H3: (wf3 g (CHead c2 (Bind b) 
-u) c0)).(let H_x \def (wf3_gen_bind1 g c2 c0 u b H3) in (let H4 \def H_x in 
-(or_ind (ex3_2 C T (\lambda (c4: C).(\lambda (_: T).(eq C c0 (CHead c4 (Bind 
-b) u)))) (\lambda (c4: C).(\lambda (_: T).(wf3 g c2 c4))) (\lambda (_: 
-C).(\lambda (w: T).(ty3 g c2 u w)))) (ex3 C (\lambda (c4: C).(eq C c0 (CHead 
-c4 (Bind Void) (TSort O)))) (\lambda (c4: C).(wf3 g c2 c4)) (\lambda (_: 
-C).(\forall (w: T).((ty3 g c2 u w) \to False)))) (eq C (CHead c3 (Bind b) u) 
-c0) (\lambda (H5: (ex3_2 C T (\lambda (c4: C).(\lambda (_: T).(eq C c0 (CHead 
-c4 (Bind b) u)))) (\lambda (c4: C).(\lambda (_: T).(wf3 g c2 c4))) (\lambda 
-(_: C).(\lambda (w: T).(ty3 g c2 u w))))).(ex3_2_ind C T (\lambda (c4: 
-C).(\lambda (_: T).(eq C c0 (CHead c4 (Bind b) u)))) (\lambda (c4: 
-C).(\lambda (_: T).(wf3 g c2 c4))) (\lambda (_: C).(\lambda (w: T).(ty3 g c2 
-u w))) (eq C (CHead c3 (Bind b) u) c0) (\lambda (x0: C).(\lambda (x1: 
-T).(\lambda (H6: (eq C c0 (CHead x0 (Bind b) u))).(\lambda (H7: (wf3 g c2 
-x0)).(\lambda (_: (ty3 g c2 u x1)).(eq_ind_r C (CHead x0 (Bind b) u) (\lambda 
-(c4: C).(eq C (CHead c3 (Bind b) u) c4)) (f_equal3 C K T C CHead c3 x0 (Bind 
-b) (Bind b) u u (H1 x0 H7) (refl_equal K (Bind b)) (refl_equal T u)) c0 
-H6)))))) H5)) (\lambda (H5: (ex3 C (\lambda (c4: C).(eq C c0 (CHead c4 (Bind 
-Void) (TSort O)))) (\lambda (c4: C).(wf3 g c2 c4)) (\lambda (_: C).(\forall 
-(w: T).((ty3 g c2 u w) \to False))))).(ex3_ind C (\lambda (c4: C).(eq C c0 
-(CHead c4 (Bind Void) (TSort O)))) (\lambda (c4: C).(wf3 g c2 c4)) (\lambda 
-(_: C).(\forall (w: T).((ty3 g c2 u w) \to False))) (eq C (CHead c3 (Bind b) 
-u) c0) (\lambda (x0: C).(\lambda (H6: (eq C c0 (CHead x0 (Bind Void) (TSort 
-O)))).(\lambda (_: (wf3 g c2 x0)).(\lambda (H8: ((\forall (w: T).((ty3 g c2 u 
-w) \to False)))).(eq_ind_r C (CHead x0 (Bind Void) (TSort O)) (\lambda (c4: 
-C).(eq C (CHead c3 (Bind b) u) c4)) (let H_x0 \def (H8 t H2) in (let H9 \def 
-H_x0 in (False_ind (eq C (CHead c3 (Bind b) u) (CHead x0 (Bind Void) (TSort 
-O))) H9))) c0 H6))))) H5)) H4))))))))))))) (\lambda (c2: C).(\lambda (c3: 
-C).(\lambda (_: (wf3 g c2 c3)).(\lambda (H1: ((\forall (c4: C).((wf3 g c2 c4) 
-\to (eq C c3 c4))))).(\lambda (u: T).(\lambda (H2: ((\forall (t: T).((ty3 g 
-c2 u t) \to False)))).(\lambda (b: B).(\lambda (c0: C).(\lambda (H3: (wf3 g 
-(CHead c2 (Bind b) u) c0)).(let H_x \def (wf3_gen_bind1 g c2 c0 u b H3) in 
-(let H4 \def H_x in (or_ind (ex3_2 C T (\lambda (c4: C).(\lambda (_: T).(eq C 
-c0 (CHead c4 (Bind b) u)))) (\lambda (c4: C).(\lambda (_: T).(wf3 g c2 c4))) 
-(\lambda (_: C).(\lambda (w: T).(ty3 g c2 u w)))) (ex3 C (\lambda (c4: C).(eq 
-C c0 (CHead c4 (Bind Void) (TSort O)))) (\lambda (c4: C).(wf3 g c2 c4)) 
-(\lambda (_: C).(\forall (w: T).((ty3 g c2 u w) \to False)))) (eq C (CHead c3 
-(Bind Void) (TSort O)) c0) (\lambda (H5: (ex3_2 C T (\lambda (c4: C).(\lambda 
-(_: T).(eq C c0 (CHead c4 (Bind b) u)))) (\lambda (c4: C).(\lambda (_: 
-T).(wf3 g c2 c4))) (\lambda (_: C).(\lambda (w: T).(ty3 g c2 u 
-w))))).(ex3_2_ind C T (\lambda (c4: C).(\lambda (_: T).(eq C c0 (CHead c4 
-(Bind b) u)))) (\lambda (c4: C).(\lambda (_: T).(wf3 g c2 c4))) (\lambda (_: 
-C).(\lambda (w: T).(ty3 g c2 u w))) (eq C (CHead c3 (Bind Void) (TSort O)) 
-c0) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (eq C c0 (CHead x0 (Bind 
-b) u))).(\lambda (_: (wf3 g c2 x0)).(\lambda (H8: (ty3 g c2 u x1)).(eq_ind_r 
-C (CHead x0 (Bind b) u) (\lambda (c4: C).(eq C (CHead c3 (Bind Void) (TSort 
-O)) c4)) (let H_x0 \def (H2 x1 H8) in (let H9 \def H_x0 in (False_ind (eq C 
-(CHead c3 (Bind Void) (TSort O)) (CHead x0 (Bind b) u)) H9))) c0 H6)))))) 
-H5)) (\lambda (H5: (ex3 C (\lambda (c4: C).(eq C c0 (CHead c4 (Bind Void) 
-(TSort O)))) (\lambda (c4: C).(wf3 g c2 c4)) (\lambda (_: C).(\forall (w: 
-T).((ty3 g c2 u w) \to False))))).(ex3_ind C (\lambda (c4: C).(eq C c0 (CHead 
-c4 (Bind Void) (TSort O)))) (\lambda (c4: C).(wf3 g c2 c4)) (\lambda (_: 
-C).(\forall (w: T).((ty3 g c2 u w) \to False))) (eq C (CHead c3 (Bind Void) 
-(TSort O)) c0) (\lambda (x0: C).(\lambda (H6: (eq C c0 (CHead x0 (Bind Void) 
-(TSort O)))).(\lambda (H7: (wf3 g c2 x0)).(\lambda (_: ((\forall (w: T).((ty3 
-g c2 u w) \to False)))).(eq_ind_r C (CHead x0 (Bind Void) (TSort O)) (\lambda 
-(c4: C).(eq C (CHead c3 (Bind Void) (TSort O)) c4)) (f_equal3 C K T C CHead 
-c3 x0 (Bind Void) (Bind Void) (TSort O) (TSort O) (H1 x0 H7) (refl_equal K 
-(Bind Void)) (refl_equal T (TSort O))) c0 H6))))) H5)) H4)))))))))))) 
-(\lambda (c2: C).(\lambda (c3: C).(\lambda (_: (wf3 g c2 c3)).(\lambda (H1: 
-((\forall (c4: C).((wf3 g c2 c4) \to (eq C c3 c4))))).(\lambda (u: 
-T).(\lambda (f: F).(\lambda (c0: C).(\lambda (H2: (wf3 g (CHead c2 (Flat f) 
-u) c0)).(let H_y \def (wf3_gen_flat1 g c2 c0 u f H2) in (H1 c0 H_y)))))))))) 
-c c1 H)))).
-(* COMMENTS
-Initial nodes: 1555
-END *)
-
-theorem wf3_total:
+lemma wf3_total:
  \forall (g: G).(\forall (c1: C).(ex C (\lambda (c2: C).(wf3 g c1 c2))))
 \def
  \lambda (g: G).(\lambda (c1: C).(C_ind (\lambda (c: C).(ex C (\lambda (c2: 
@@ -120,11 +40,8 @@ False)))).(ex_intro C (\lambda (c2: C).(wf3 g (CHead c (Bind b) t) c2))
 (CHead x (Bind Void) (TSort O)) (wf3_void g c x H1 t H3 b))) H2)))) (\lambda 
 (f: F).(ex_intro C (\lambda (c2: C).(wf3 g (CHead c (Flat f) t) c2)) x 
 (wf3_flat g c x H1 t f))) k))) H0)))))) c1)).
-(* COMMENTS
-Initial nodes: 435
-END *)
 
-theorem ty3_shift1:
+lemma ty3_shift1:
  \forall (g: G).(\forall (c: C).((wf3 g c c) \to (\forall (t1: T).(\forall 
 (t2: T).((ty3 g c t1 t2) \to (ty3 g (CSort (cbk c)) (app1 c t1) (app1 c 
 t2)))))))
@@ -143,32 +60,30 @@ c1 c2) \to (\forall (t1: T).(\forall (t2: T).((ty3 g c1 t1 t2) \to (ty3 g
 (t: T).(\lambda (H3: (ty3 g c1 u t)).(\lambda (b: B).(\lambda (H4: (eq C 
 (CHead c1 (Bind b) u) (CHead c2 (Bind b) u))).(\lambda (t1: T).(\lambda (t2: 
 T).(\lambda (H5: (ty3 g (CHead c1 (Bind b) u) t1 t2)).(let H6 \def (f_equal C 
-C (\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _) 
-\Rightarrow c1 | (CHead c0 _ _) \Rightarrow c0])) (CHead c1 (Bind b) u) 
-(CHead c2 (Bind b) u) H4) in (let H7 \def (eq_ind_r C c2 (\lambda (c0: 
-C).((eq C c1 c0) \to (\forall (t3: T).(\forall (t4: T).((ty3 g c1 t3 t4) \to 
-(ty3 g (CSort (cbk c1)) (app1 c1 t3) (app1 c1 t4))))))) H2 c1 H6) in (let H8 
-\def (eq_ind_r C c2 (\lambda (c0: C).(wf3 g c1 c0)) H1 c1 H6) in (ex_ind T 
-(\lambda (t0: T).(ty3 g (CHead c1 (Bind b) u) t2 t0)) (ty3 g (CSort (cbk c1)) 
-(app1 c1 (THead (Bind b) u t1)) (app1 c1 (THead (Bind b) u t2))) (\lambda (x: 
-T).(\lambda (_: (ty3 g (CHead c1 (Bind b) u) t2 x)).(H7 (refl_equal C c1) 
-(THead (Bind b) u t1) (THead (Bind b) u t2) (ty3_bind g c1 u t H3 b t1 t2 
-H5)))) (ty3_correct g (CHead c1 (Bind b) u) t1 t2 H5))))))))))))))))) 
-(\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (wf3 g c1 c2)).(\lambda (H2: 
-(((eq C c1 c2) \to (\forall (t1: T).(\forall (t2: T).((ty3 g c1 t1 t2) \to 
-(ty3 g (CSort (cbk c1)) (app1 c1 t1) (app1 c1 t2)))))))).(\lambda (u: 
-T).(\lambda (H3: ((\forall (t: T).((ty3 g c1 u t) \to False)))).(\lambda (b: 
-B).(\lambda (H4: (eq C (CHead c1 (Bind b) u) (CHead c2 (Bind Void) (TSort 
-O)))).(\lambda (t1: T).(\lambda (t2: T).(\lambda (H5: (ty3 g (CHead c1 (Bind 
-b) u) t1 t2)).(let H6 \def (f_equal C C (\lambda (e: C).(match e in C return 
-(\lambda (_: C).C) with [(CSort _) \Rightarrow c1 | (CHead c0 _ _) 
-\Rightarrow c0])) (CHead c1 (Bind b) u) (CHead c2 (Bind Void) (TSort O)) H4) 
-in ((let H7 \def (f_equal C B (\lambda (e: C).(match e in C return (\lambda 
-(_: C).B) with [(CSort _) \Rightarrow b | (CHead _ k _) \Rightarrow (match k 
-in K return (\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _) 
-\Rightarrow b])])) (CHead c1 (Bind b) u) (CHead c2 (Bind Void) (TSort O)) H4) 
-in ((let H8 \def (f_equal C T (\lambda (e: C).(match e in C return (\lambda 
-(_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t])) 
+C (\lambda (e: C).(match e with [(CSort _) \Rightarrow c1 | (CHead c0 _ _) 
+\Rightarrow c0])) (CHead c1 (Bind b) u) (CHead c2 (Bind b) u) H4) in (let H7 
+\def (eq_ind_r C c2 (\lambda (c0: C).((eq C c1 c0) \to (\forall (t3: 
+T).(\forall (t4: T).((ty3 g c1 t3 t4) \to (ty3 g (CSort (cbk c1)) (app1 c1 
+t3) (app1 c1 t4))))))) H2 c1 H6) in (let H8 \def (eq_ind_r C c2 (\lambda (c0: 
+C).(wf3 g c1 c0)) H1 c1 H6) in (ex_ind T (\lambda (t0: T).(ty3 g (CHead c1 
+(Bind b) u) t2 t0)) (ty3 g (CSort (cbk c1)) (app1 c1 (THead (Bind b) u t1)) 
+(app1 c1 (THead (Bind b) u t2))) (\lambda (x: T).(\lambda (_: (ty3 g (CHead 
+c1 (Bind b) u) t2 x)).(H7 (refl_equal C c1) (THead (Bind b) u t1) (THead 
+(Bind b) u t2) (ty3_bind g c1 u t H3 b t1 t2 H5)))) (ty3_correct g (CHead c1 
+(Bind b) u) t1 t2 H5))))))))))))))))) (\lambda (c1: C).(\lambda (c2: 
+C).(\lambda (H1: (wf3 g c1 c2)).(\lambda (H2: (((eq C c1 c2) \to (\forall 
+(t1: T).(\forall (t2: T).((ty3 g c1 t1 t2) \to (ty3 g (CSort (cbk c1)) (app1 
+c1 t1) (app1 c1 t2)))))))).(\lambda (u: T).(\lambda (H3: ((\forall (t: 
+T).((ty3 g c1 u t) \to False)))).(\lambda (b: B).(\lambda (H4: (eq C (CHead 
+c1 (Bind b) u) (CHead c2 (Bind Void) (TSort O)))).(\lambda (t1: T).(\lambda 
+(t2: T).(\lambda (H5: (ty3 g (CHead c1 (Bind b) u) t1 t2)).(let H6 \def 
+(f_equal C C (\lambda (e: C).(match e with [(CSort _) \Rightarrow c1 | (CHead 
+c0 _ _) \Rightarrow c0])) (CHead c1 (Bind b) u) (CHead c2 (Bind Void) (TSort 
+O)) H4) in ((let H7 \def (f_equal C B (\lambda (e: C).(match e with [(CSort 
+_) \Rightarrow b | (CHead _ k _) \Rightarrow (match k with [(Bind b0) 
+\Rightarrow b0 | (Flat _) \Rightarrow b])])) (CHead c1 (Bind b) u) (CHead c2 
+(Bind Void) (TSort O)) H4) in ((let H8 \def (f_equal C T (\lambda (e: 
+C).(match e with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t])) 
 (CHead c1 (Bind b) u) (CHead c2 (Bind Void) (TSort O)) H4) in (\lambda (H9: 
 (eq B b Void)).(\lambda (H10: (eq C c1 c2)).(let H11 \def (eq_ind B b 
 (\lambda (b0: B).(ty3 g (CHead c1 (Bind b0) u) t1 t2)) H5 Void H9) in 
@@ -203,16 +118,12 @@ c0) \to (\forall (t3: T).(\forall (t4: T).((ty3 g c1 t3 t4) \to (ty3 g (CSort
 (let H8 \def H_x in (ex_ind B (\lambda (b: B).(eq K (Flat f) (Bind b))) (ty3 
 g (CSort (cbk c1)) (app1 c1 (THead (Flat f) u t1)) (app1 c1 (THead (Flat f) u 
 t2))) (\lambda (x: B).(\lambda (H9: (eq K (Flat f) (Bind x))).(let H10 \def 
-(eq_ind K (Flat f) (\lambda (ee: K).(match ee in K return (\lambda (_: 
-K).Prop) with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow True])) I 
-(Bind x) H9) in (False_ind (ty3 g (CSort (cbk c1)) (app1 c1 (THead (Flat f) u 
-t1)) (app1 c1 (THead (Flat f) u t2))) H10)))) H8)))))))))))))))) y c H0))) 
-H))).
-(* COMMENTS
-Initial nodes: 1677
-END *)
+(eq_ind K (Flat f) (\lambda (ee: K).(match ee with [(Bind _) \Rightarrow 
+False | (Flat _) \Rightarrow True])) I (Bind x) H9) in (False_ind (ty3 g 
+(CSort (cbk c1)) (app1 c1 (THead (Flat f) u t1)) (app1 c1 (THead (Flat f) u 
+t2))) H10)))) H8)))))))))))))))) y c H0))) H))).
 
-theorem wf3_idem:
+lemma wf3_idem:
  \forall (g: G).(\forall (c1: C).(\forall (c2: C).((wf3 g c1 c2) \to (wf3 g 
 c2 c2))))
 \def
@@ -227,11 +138,8 @@ c3 u t H2 c4 H0) b))))))))) (\lambda (c3: C).(\lambda (c4: C).(\lambda (_:
 c4 H1 (TSort O) (TSort (next g O)) (ty3_sort g c4 O) Void)))))))) (\lambda 
 (c3: C).(\lambda (c4: C).(\lambda (_: (wf3 g c3 c4)).(\lambda (H1: (wf3 g c4 
 c4)).(\lambda (_: T).(\lambda (_: F).H1)))))) c1 c2 H)))).
-(* COMMENTS
-Initial nodes: 207
-END *)
 
-theorem wf3_ty3:
+lemma wf3_ty3:
  \forall (g: G).(\forall (c1: C).(\forall (t: T).(\forall (u: T).((ty3 g c1 t 
 u) \to (ex2 C (\lambda (c2: C).(wf3 g c1 c2)) (\lambda (c2: C).(ty3 g c2 t 
 u)))))))
@@ -242,7 +150,4 @@ C (\lambda (c2: C).(wf3 g c1 c2)) (ex2 C (\lambda (c2: C).(wf3 g c1 c2))
 (\lambda (c2: C).(ty3 g c2 t u))) (\lambda (x: C).(\lambda (H1: (wf3 g c1 
 x)).(ex_intro2 C (\lambda (c2: C).(wf3 g c1 c2)) (\lambda (c2: C).(ty3 g c2 t 
 u)) x H1 (wf3_ty3_conf g c1 t u H x H1)))) H0))))))).
-(* COMMENTS
-Initial nodes: 123
-END *)