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[helm.git] / helm / software / matita / contribs / LAMBDA-TYPES / LambdaDelta-1 / ty3 / props.ma

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/ty3/props.ma b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/ty3/props.ma
index 053b5d67714f8f3c9c2d9ff6ba316dd048573960..7fbddf8ebfd72f55b0badcc4430a216a18cb22f1 100644 (file)
--- a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/ty3/props.ma
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/ty3/props.ma
@@ -14,10 +14,12 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-set "baseuri" "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/ty3/props".
+
 
 include "ty3/fwd.ma".
 
+include "pc3/fwd.ma".
+
 theorem ty3_lift:
  \forall (g: G).(\forall (e: C).(\forall (t1: T).(\forall (t2: T).((ty3 g e 
 t1 t2) \to (\forall (c: C).(\forall (d: nat).(\forall (h: nat).((drop h d c 
@@ -177,10 +179,14 @@ C).(\lambda (t0: T).(\lambda (t3: T).(\lambda (_: (ty3 g c t0 t3)).(\lambda
 nat).(\forall (h: nat).((drop h d c0 c) \to (ty3 g c0 (lift h d t3) (lift h d 
 t4)))))))).(\lambda (c0: C).(\lambda (d: nat).(\lambda (h: nat).(\lambda (H4: 
 (drop h d c0 c)).(eq_ind_r T (THead (Flat Cast) (lift h d t3) (lift h (s 
-(Flat Cast) d) t0)) (\lambda (t: T).(ty3 g c0 t (lift h d t3))) (ty3_cast g 
-c0 (lift h (s (Flat Cast) d) t0) (lift h d t3) (H1 c0 d h H4) (lift h d t4) 
-(H3 c0 d h H4)) (lift h d (THead (Flat Cast) t3 t0)) (lift_head (Flat Cast) 
-t3 t0 h d)))))))))))))) e t1 t2 H))))).
+(Flat Cast) d) t0)) (\lambda (t: T).(ty3 g c0 t (lift h d (THead (Flat Cast) 
+t4 t3)))) (eq_ind_r T (THead (Flat Cast) (lift h d t4) (lift h (s (Flat Cast) 
+d) t3)) (\lambda (t: T).(ty3 g c0 (THead (Flat Cast) (lift h d t3) (lift h (s 
+(Flat Cast) d) t0)) t)) (ty3_cast g c0 (lift h (s (Flat Cast) d) t0) (lift h 
+(s (Flat Cast) d) t3) (H1 c0 (s (Flat Cast) d) h H4) (lift h d t4) (H3 c0 d h 
+H4)) (lift h d (THead (Flat Cast) t4 t3)) (lift_head (Flat Cast) t4 t3 h d)) 
+(lift h d (THead (Flat Cast) t3 t0)) (lift_head (Flat Cast) t3 t0 h 
+d)))))))))))))) e t1 t2 H))))).
 
 theorem ty3_correct:
  \forall (g: G).(\forall (c: C).(\forall (t1: T).(\forall (t2: T).((ty3 g c 
@@ -242,10 +248,14 @@ T).(ty3 g c0 (THead (Flat Appl) w (THead (Bind Abst) u t)) t0)) (THead (Flat
 Appl) w (THead (Bind Abst) u x1)) (ty3_appl g c0 w u H0 (THead (Bind Abst) u 
 t) x1 (ty3_bind g c0 u x2 H9 Abst t x1 H10 x3 H11)))))))))) (ty3_gen_bind g 
 Abst c0 u t x0 H7)))) H6)))) H4))))))))))) (\lambda (c0: C).(\lambda (t0: 
-T).(\lambda (t3: T).(\lambda (_: (ty3 g c0 t0 t3)).(\lambda (H1: (ex T 
-(\lambda (t: T).(ty3 g c0 t3 t)))).(\lambda (t4: T).(\lambda (_: (ty3 g c0 t3 
-t4)).(\lambda (_: (ex T (\lambda (t: T).(ty3 g c0 t4 t)))).H1)))))))) c t1 t2 
-H))))).
+T).(\lambda (t3: T).(\lambda (_: (ty3 g c0 t0 t3)).(\lambda (_: (ex T 
+(\lambda (t: T).(ty3 g c0 t3 t)))).(\lambda (t4: T).(\lambda (H2: (ty3 g c0 
+t3 t4)).(\lambda (H3: (ex T (\lambda (t: T).(ty3 g c0 t4 t)))).(let H4 \def 
+H3 in (ex_ind T (\lambda (t: T).(ty3 g c0 t4 t)) (ex T (\lambda (t: T).(ty3 g 
+c0 (THead (Flat Cast) t4 t3) t))) (\lambda (x: T).(\lambda (H5: (ty3 g c0 t4 
+x)).(ex_intro T (\lambda (t: T).(ty3 g c0 (THead (Flat Cast) t4 t3) t)) 
+(THead (Flat Cast) x t4) (ty3_cast g c0 t3 t4 H2 x H5)))) H4)))))))))) c t1 
+t2 H))))).
 
 theorem ty3_unique:
  \forall (g: G).(\forall (c: C).(\forall (u: T).(\forall (t1: T).((ty3 g c u 
@@ -414,9 +424,60 @@ x1) (H3 (THead (Bind Abst) x0 x1) H6) w Appl) t2 H5)))))) (ty3_gen_appl g c0
 w v t2 H4))))))))))))) (\lambda (c0: C).(\lambda (t0: T).(\lambda (t2: 
 T).(\lambda (_: (ty3 g c0 t0 t2)).(\lambda (_: ((\forall (t3: T).((ty3 g c0 
 t0 t3) \to (pc3 c0 t2 t3))))).(\lambda (t3: T).(\lambda (_: (ty3 g c0 t2 
-t3)).(\lambda (_: ((\forall (t4: T).((ty3 g c0 t2 t4) \to (pc3 c0 t3 
+t3)).(\lambda (H3: ((\forall (t4: T).((ty3 g c0 t2 t4) \to (pc3 c0 t3 
 t4))))).(\lambda (t4: T).(\lambda (H4: (ty3 g c0 (THead (Flat Cast) t2 t0) 
-t4)).(and_ind (pc3 c0 t2 t4) (ty3 g c0 t0 t2) (pc3 c0 t2 t4) (\lambda (H5: 
-(pc3 c0 t2 t4)).(\lambda (_: (ty3 g c0 t0 t2)).H5)) (ty3_gen_cast g c0 t0 t2 
-t4 H4)))))))))))) c u t1 H))))).
+t4)).(ex3_ind T (\lambda (t5: T).(pc3 c0 (THead (Flat Cast) t5 t2) t4)) 
+(\lambda (_: T).(ty3 g c0 t0 t2)) (\lambda (t5: T).(ty3 g c0 t2 t5)) (pc3 c0 
+(THead (Flat Cast) t3 t2) t4) (\lambda (x0: T).(\lambda (H5: (pc3 c0 (THead 
+(Flat Cast) x0 t2) t4)).(\lambda (_: (ty3 g c0 t0 t2)).(\lambda (H7: (ty3 g 
+c0 t2 x0)).(pc3_t (THead (Flat Cast) x0 t2) c0 (THead (Flat Cast) t3 t2) 
+(pc3_head_1 c0 t3 x0 (H3 x0 H7) (Flat Cast) t2) t4 H5))))) (ty3_gen_cast g c0 
+t0 t2 t4 H4)))))))))))) c u t1 H))))).
+
+theorem ty3_gen_abst_abst:
+ \forall (g: G).(\forall (c: C).(\forall (u: T).(\forall (t1: T).(\forall 
+(t2: T).((ty3 g c (THead (Bind Abst) u t1) (THead (Bind Abst) u t2)) \to (ex2 
+T (\lambda (w: T).(ty3 g c u w)) (\lambda (_: T).(ty3 g (CHead c (Bind Abst) 
+u) t1 t2))))))))
+\def
+ \lambda (g: G).(\lambda (c: C).(\lambda (u: T).(\lambda (t1: T).(\lambda 
+(t2: T).(\lambda (H: (ty3 g c (THead (Bind Abst) u t1) (THead (Bind Abst) u 
+t2))).(ex_ind T (\lambda (t: T).(ty3 g c (THead (Bind Abst) u t2) t)) (ex2 T 
+(\lambda (w: T).(ty3 g c u w)) (\lambda (_: T).(ty3 g (CHead c (Bind Abst) u) 
+t1 t2))) (\lambda (x: T).(\lambda (H0: (ty3 g c (THead (Bind Abst) u t2) 
+x)).(ex4_3_ind T T T (\lambda (t3: T).(\lambda (_: T).(\lambda (_: T).(pc3 c 
+(THead (Bind Abst) u t3) x)))) (\lambda (_: T).(\lambda (t: T).(\lambda (_: 
+T).(ty3 g c u t)))) (\lambda (t3: T).(\lambda (_: T).(\lambda (_: T).(ty3 g 
+(CHead c (Bind Abst) u) t2 t3)))) (\lambda (t3: T).(\lambda (_: T).(\lambda 
+(t0: T).(ty3 g (CHead c (Bind Abst) u) t3 t0)))) (ex2 T (\lambda (w: T).(ty3 
+g c u w)) (\lambda (_: T).(ty3 g (CHead c (Bind Abst) u) t1 t2))) (\lambda 
+(x0: T).(\lambda (x1: T).(\lambda (x2: T).(\lambda (_: (pc3 c (THead (Bind 
+Abst) u x0) x)).(\lambda (H2: (ty3 g c u x1)).(\lambda (H3: (ty3 g (CHead c 
+(Bind Abst) u) t2 x0)).(\lambda (_: (ty3 g (CHead c (Bind Abst) u) x0 
+x2)).(ex4_3_ind T T T (\lambda (t3: T).(\lambda (_: T).(\lambda (_: T).(pc3 c 
+(THead (Bind Abst) u t3) (THead (Bind Abst) u t2))))) (\lambda (_: 
+T).(\lambda (t: T).(\lambda (_: T).(ty3 g c u t)))) (\lambda (t3: T).(\lambda 
+(_: T).(\lambda (_: T).(ty3 g (CHead c (Bind Abst) u) t1 t3)))) (\lambda (t3: 
+T).(\lambda (_: T).(\lambda (t0: T).(ty3 g (CHead c (Bind Abst) u) t3 t0)))) 
+(ex2 T (\lambda (w: T).(ty3 g c u w)) (\lambda (_: T).(ty3 g (CHead c (Bind 
+Abst) u) t1 t2))) (\lambda (x3: T).(\lambda (x4: T).(\lambda (x5: T).(\lambda 
+(H5: (pc3 c (THead (Bind Abst) u x3) (THead (Bind Abst) u t2))).(\lambda (_: 
+(ty3 g c u x4)).(\lambda (H7: (ty3 g (CHead c (Bind Abst) u) t1 x3)).(\lambda 
+(_: (ty3 g (CHead c (Bind Abst) u) x3 x5)).(let H_y \def (pc3_gen_abst_shift 
+c u x3 t2 H5) in (ex_intro2 T (\lambda (w: T).(ty3 g c u w)) (\lambda (_: 
+T).(ty3 g (CHead c (Bind Abst) u) t1 t2)) x1 H2 (ty3_conv g (CHead c (Bind 
+Abst) u) t2 x0 H3 t1 x3 H7 H_y)))))))))) (ty3_gen_bind g Abst c u t1 (THead 
+(Bind Abst) u t2) H))))))))) (ty3_gen_bind g Abst c u t2 x H0)))) 
+(ty3_correct g c (THead (Bind Abst) u t1) (THead (Bind Abst) u t2) H))))))).
+
+theorem ty3_typecheck:
+ \forall (g: G).(\forall (c: C).(\forall (t: T).(\forall (v: T).((ty3 g c t 
+v) \to (ex T (\lambda (u: T).(ty3 g c (THead (Flat Cast) v t) u)))))))
+\def
+ \lambda (g: G).(\lambda (c: C).(\lambda (t: T).(\lambda (v: T).(\lambda (H: 
+(ty3 g c t v)).(ex_ind T (\lambda (t0: T).(ty3 g c v t0)) (ex T (\lambda (u: 
+T).(ty3 g c (THead (Flat Cast) v t) u))) (\lambda (x: T).(\lambda (H0: (ty3 g 
+c v x)).(ex_intro T (\lambda (u: T).(ty3 g c (THead (Flat Cast) v t) u)) 
+(THead (Flat Cast) x v) (ty3_cast g c t v H x H0)))) (ty3_correct g c t v 
+H)))))).