Procedural : tentative update to the new letin cic construction

[helm.git] / helm / software / matita / contribs / LAMBDA-TYPES / LambdaDelta-1 / sn3 / props.ma

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/sn3/props.ma b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/sn3/props.ma
index 254589a2768588a3f4c6dc3696cc0c4a71cb0652..9341f979b3a103bcbb8de7447fa361bd4ec8dc80 100644 (file)
--- a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/sn3/props.ma
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/sn3/props.ma
@@ -157,7 +157,7 @@ theorem sn3_shift:
 \def
  \lambda (b: B).(\lambda (c: C).(\lambda (v: T).(\lambda (t: T).(\lambda (H: 
 (sn3 c (THead (Bind b) v t))).(let H_x \def (sn3_gen_bind b c v t H) in (let 
-H0 \def H_x in (and_ind (sn3 c v) (sn3 (CHead c (Bind b) v) t) (sn3 (CHead c 
+H0 \def H_x in (land_ind (sn3 c v) (sn3 (CHead c (Bind b) v) t) (sn3 (CHead c 
 (Bind b) v) t) (\lambda (_: (sn3 c v)).(\lambda (H2: (sn3 (CHead c (Bind b) 
 v) t)).H2)) H0))))))).
 
@@ -223,7 +223,7 @@ c (THead k0 u t1)) \to (sn3 d v0))))) (\lambda (b: B).(\lambda (_: (subst0 (s
 (Bind b) i0) v0 t1 t2)).(\lambda (H7: ((\forall (c0: C).(\forall (d0: 
 C).((getl (s (Bind b) i0) c0 (CHead d0 (Bind Abbr) v0)) \to ((sn3 c0 t1) \to 
 (sn3 d0 v0))))))).(\lambda (H8: (sn3 c (THead (Bind b) u t1))).(let H_x0 \def 
-(sn3_gen_bind b c u t1 H8) in (let H9 \def H_x0 in (and_ind (sn3 c u) (sn3 
+(sn3_gen_bind b c u t1 H8) in (let H9 \def H_x0 in (land_ind (sn3 c u) (sn3 
 (CHead c (Bind b) u) t1) (sn3 d v0) (\lambda (_: (sn3 c u)).(\lambda (H11: 
 (sn3 (CHead c (Bind b) u) t1)).(H7 (CHead c (Bind b) u) d (getl_clear_bind b 
 (CHead c (Bind b) u) c u (clear_bind b c u) (CHead d (Bind Abbr) v0) i0 H4) 
@@ -231,8 +231,8 @@ H11))) H9))))))) (\lambda (f: F).(\lambda (_: (subst0 (s (Flat f) i0) v0 t1
 t2)).(\lambda (H7: ((\forall (c0: C).(\forall (d0: C).((getl (s (Flat f) i0) 
 c0 (CHead d0 (Bind Abbr) v0)) \to ((sn3 c0 t1) \to (sn3 d0 v0))))))).(\lambda 
 (H8: (sn3 c (THead (Flat f) u t1))).(let H_x0 \def (sn3_gen_flat f c u t1 H8) 
-in (let H9 \def H_x0 in (and_ind (sn3 c u) (sn3 c t1) (sn3 d v0) (\lambda (_: 
-(sn3 c u)).(\lambda (H11: (sn3 c t1)).(H7 c d H4 H11))) H9))))))) k H2 H3 
+in (let H9 \def H_x0 in (land_ind (sn3 c u) (sn3 c t1) (sn3 d v0) (\lambda 
+(_: (sn3 c u)).(\lambda (H11: (sn3 c t1)).(H7 c d H4 H11))) H9))))))) k H2 H3 
 H5))))))))))))) (\lambda (v0: T).(\lambda (u1: T).(\lambda (u2: T).(\lambda 
 (i0: nat).(\lambda (_: (subst0 i0 v0 u1 u2)).(\lambda (H3: ((\forall (c: 
 C).(\forall (d: C).((getl i0 c (CHead d (Bind Abbr) v0)) \to ((sn3 c u1) \to 
@@ -2165,7 +2165,7 @@ t))))))))))
  \lambda (c: C).(\lambda (u: T).(\lambda (v: T).(\lambda (t: T).(\lambda (H: 
 (sn3 c (THead (Flat Appl) u (THead (Bind Abbr) v t)))).(\lambda (w: 
 T).(\lambda (H0: (sn3 c w)).(let H_x \def (sn3_gen_flat Appl c u (THead (Bind 
-Abbr) v t) H) in (let H1 \def H_x in (and_ind (sn3 c u) (sn3 c (THead (Bind 
+Abbr) v t) H) in (let H1 \def H_x in (land_ind (sn3 c u) (sn3 c (THead (Bind 
 Abbr) v t)) (sn3 c (THead (Flat Appl) u (THead (Flat Appl) v (THead (Bind 
 Abst) w t)))) (\lambda (H2: (sn3 c u)).(\lambda (H3: (sn3 c (THead (Bind 
 Abbr) v t))).(sn3_appl_appl v (THead (Bind Abst) w t) c (sn3_beta c v t H3 w 
@@ -2204,17 +2204,17 @@ c t1) \to (sn3 c (THeads (Flat Appl) t1 (TLRef i))))) \to ((land (sn3 c t)
 (sns3 c t1)) \to (sn3 c (THead (Flat Appl) t (THeads (Flat Appl) t1 (TLRef 
 i))))))) (\lambda (_: (((sns3 c TNil) \to (sn3 c (THeads (Flat Appl) TNil 
 (TLRef i)))))).(\lambda (H1: (land (sn3 c t) (sns3 c TNil))).(let H2 \def H1 
-in (and_ind (sn3 c t) True (sn3 c (THead (Flat Appl) t (THeads (Flat Appl) 
+in (land_ind (sn3 c t) True (sn3 c (THead (Flat Appl) t (THeads (Flat Appl) 
 TNil (TLRef i)))) (\lambda (H3: (sn3 c t)).(\lambda (_: True).(sn3_appl_lref 
 c i H t H3))) H2)))) (\lambda (t1: T).(\lambda (t2: TList).(\lambda (_: 
 (((((sns3 c t2) \to (sn3 c (THeads (Flat Appl) t2 (TLRef i))))) \to ((land 
 (sn3 c t) (sns3 c t2)) \to (sn3 c (THead (Flat Appl) t (THeads (Flat Appl) t2 
 (TLRef i)))))))).(\lambda (H1: (((sns3 c (TCons t1 t2)) \to (sn3 c (THeads 
 (Flat Appl) (TCons t1 t2) (TLRef i)))))).(\lambda (H2: (land (sn3 c t) (sns3 
-c (TCons t1 t2)))).(let H3 \def H2 in (and_ind (sn3 c t) (land (sn3 c t1) 
+c (TCons t1 t2)))).(let H3 \def H2 in (land_ind (sn3 c t) (land (sn3 c t1) 
 (sns3 c t2)) (sn3 c (THead (Flat Appl) t (THeads (Flat Appl) (TCons t1 t2) 
 (TLRef i)))) (\lambda (H4: (sn3 c t)).(\lambda (H5: (land (sn3 c t1) (sns3 c 
-t2))).(and_ind (sn3 c t1) (sns3 c t2) (sn3 c (THead (Flat Appl) t (THeads 
+t2))).(land_ind (sn3 c t1) (sns3 c t2) (sn3 c (THead (Flat Appl) t (THeads 
 (Flat Appl) (TCons t1 t2) (TLRef i)))) (\lambda (H6: (sn3 c t1)).(\lambda 
 (H7: (sns3 c t2)).(sn3_appl_appls t1 (TLRef i) t2 c (H1 (conj (sn3 c t1) 
 (sns3 c t2) H6 H7)) t H4 (\lambda (u2: T).(\lambda (H8: (pr3 c (THeads (Flat 
@@ -2258,22 +2258,22 @@ t3))))))))).(\lambda (u: T).(\lambda (H1: (sn3 c (THead (Flat Appl) t (THeads
 (Flat Appl) (TCons t1 t2) u)))).(\lambda (t3: T).(\lambda (H2: (sn3 c (THead 
 (Flat Appl) t (THeads (Flat Appl) (TCons t1 t2) t3)))).(let H_x \def 
 (sn3_gen_flat Appl c t (THeads (Flat Appl) (TCons t1 t2) t3) H2) in (let H3 
-\def H_x in (and_ind (sn3 c t) (sn3 c (THeads (Flat Appl) (TCons t1 t2) t3)) 
+\def H_x in (land_ind (sn3 c t) (sn3 c (THeads (Flat Appl) (TCons t1 t2) t3)) 
 (sn3 c (THead (Flat Appl) t (THeads (Flat Appl) (TCons t1 t2) (THead (Flat 
 Cast) u t3)))) (\lambda (_: (sn3 c t)).(\lambda (H5: (sn3 c (THeads (Flat 
 Appl) (TCons t1 t2) t3))).(let H6 \def H5 in (let H_x0 \def (sn3_gen_flat 
 Appl c t (THeads (Flat Appl) (TCons t1 t2) u) H1) in (let H7 \def H_x0 in 
-(and_ind (sn3 c t) (sn3 c (THeads (Flat Appl) (TCons t1 t2) u)) (sn3 c (THead 
-(Flat Appl) t (THeads (Flat Appl) (TCons t1 t2) (THead (Flat Cast) u t3)))) 
-(\lambda (H8: (sn3 c t)).(\lambda (H9: (sn3 c (THeads (Flat Appl) (TCons t1 
-t2) u))).(let H10 \def H9 in (sn3_appl_appls t1 (THead (Flat Cast) u t3) t2 c 
-(H0 u H10 t3 H6) t H8 (\lambda (u2: T).(\lambda (H11: (pr3 c (THeads (Flat 
-Appl) (TCons t1 t2) (THead (Flat Cast) u t3)) u2)).(\lambda (H12: (((iso 
-(THeads (Flat Appl) (TCons t1 t2) (THead (Flat Cast) u t3)) u2) \to (\forall 
-(P: Prop).P)))).(sn3_pr3_trans c (THead (Flat Appl) t (THeads (Flat Appl) 
-(TCons t1 t2) t3)) H2 (THead (Flat Appl) t u2) (pr3_thin_dx c (THeads (Flat 
-Appl) (TCons t1 t2) t3) u2 (pr3_iso_appls_cast c u t3 (TCons t1 t2) u2 H11 
-H12) t Appl))))))))) H7)))))) H3))))))))))) t0))) vs)).
+(land_ind (sn3 c t) (sn3 c (THeads (Flat Appl) (TCons t1 t2) u)) (sn3 c 
+(THead (Flat Appl) t (THeads (Flat Appl) (TCons t1 t2) (THead (Flat Cast) u 
+t3)))) (\lambda (H8: (sn3 c t)).(\lambda (H9: (sn3 c (THeads (Flat Appl) 
+(TCons t1 t2) u))).(let H10 \def H9 in (sn3_appl_appls t1 (THead (Flat Cast) 
+u t3) t2 c (H0 u H10 t3 H6) t H8 (\lambda (u2: T).(\lambda (H11: (pr3 c 
+(THeads (Flat Appl) (TCons t1 t2) (THead (Flat Cast) u t3)) u2)).(\lambda 
+(H12: (((iso (THeads (Flat Appl) (TCons t1 t2) (THead (Flat Cast) u t3)) u2) 
+\to (\forall (P: Prop).P)))).(sn3_pr3_trans c (THead (Flat Appl) t (THeads 
+(Flat Appl) (TCons t1 t2) t3)) H2 (THead (Flat Appl) t u2) (pr3_thin_dx c 
+(THeads (Flat Appl) (TCons t1 t2) t3) u2 (pr3_iso_appls_cast c u t3 (TCons t1 
+t2) u2 H11 H12) t Appl))))))))) H7)))))) H3))))))))))) t0))) vs)).
 
 theorem sn3_appls_bind:
  \forall (b: B).((not (eq B b Abst)) \to (\forall (c: C).(\forall (u: 
@@ -2308,7 +2308,7 @@ t1))))))))).(\lambda (H2: ((\forall (t1: T).((sn3 (CHead c (Bind b) u)
 T).(\lambda (H3: (sn3 (CHead c (Bind b) u) (THead (Flat Appl) (lift (S O) O 
 v) (THeads (Flat Appl) (lifts (S O) O (TCons t t0)) t1)))).(let H_x \def 
 (sn3_gen_flat Appl (CHead c (Bind b) u) (lift (S O) O v) (THeads (Flat Appl) 
-(lifts (S O) O (TCons t t0)) t1) H3) in (let H4 \def H_x in (and_ind (sn3 
+(lifts (S O) O (TCons t t0)) t1) H3) in (let H4 \def H_x in (land_ind (sn3 
 (CHead c (Bind b) u) (lift (S O) O v)) (sn3 (CHead c (Bind b) u) (THeads 
 (Flat Appl) (lifts (S O) O (TCons t t0)) t1)) (sn3 c (THead (Flat Appl) v 
 (THeads (Flat Appl) (TCons t t0) (THead (Bind b) u t1)))) (\lambda (H5: (sn3 
@@ -2361,7 +2361,7 @@ Appl) (TCons t0 t1) (THead (Bind Abbr) v t))) \to (\forall (w: T).((sn3 c w)
 (Flat Appl) (TCons t0 t1) (THead (Bind Abbr) v t))))).(\lambda (w: 
 T).(\lambda (H2: (sn3 c w)).(let H_x \def (sn3_gen_flat Appl c u (THeads 
 (Flat Appl) (TCons t0 t1) (THead (Bind Abbr) v t)) H1) in (let H3 \def H_x in 
-(and_ind (sn3 c u) (sn3 c (THeads (Flat Appl) (TCons t0 t1) (THead (Bind 
+(land_ind (sn3 c u) (sn3 c (THeads (Flat Appl) (TCons t0 t1) (THead (Bind 
 Abbr) v t))) (sn3 c (THead (Flat Appl) u (THeads (Flat Appl) (TCons t0 t1) 
 (THead (Flat Appl) v (THead (Bind Abst) w t))))) (\lambda (H4: (sn3 c 
 u)).(\lambda (H5: (sn3 c (THeads (Flat Appl) (TCons t0 t1) (THead (Bind Abbr) 
@@ -2466,7 +2466,7 @@ i)))))))).(\lambda (H1: (((sn3 c (THeads (Flat Appl) (TCons t t0) (lift (S i)
 O w))) \to (sn3 c (THeads (Flat Appl) (TCons t t0) (TLRef i)))))).(\lambda 
 (H2: (sn3 c (THead (Flat Appl) v (THeads (Flat Appl) (TCons t t0) (lift (S i) 
 O w))))).(let H_x \def (sn3_gen_flat Appl c v (THeads (Flat Appl) (TCons t 
-t0) (lift (S i) O w)) H2) in (let H3 \def H_x in (and_ind (sn3 c v) (sn3 c 
+t0) (lift (S i) O w)) H2) in (let H3 \def H_x in (land_ind (sn3 c v) (sn3 c 
 (THeads (Flat Appl) (TCons t t0) (lift (S i) O w))) (sn3 c (THead (Flat Appl) 
 v (THeads (Flat Appl) (TCons t t0) (TLRef i)))) (\lambda (H4: (sn3 c 
 v)).(\lambda (H5: (sn3 c (THeads (Flat Appl) (TCons t t0) (lift (S i) O 
@@ -2487,7 +2487,7 @@ i c d) \to (\forall (ts: TList).((sns3 d ts) \to (sns3 c (lifts h i ts))))))))
 TList).((sns3 d t) \to (sns3 c (lifts h i t)))) (\lambda (H0: True).H0) 
 (\lambda (t: T).(\lambda (t0: TList).(\lambda (H0: (((sns3 d t0) \to (sns3 c 
 (lifts h i t0))))).(\lambda (H1: (land (sn3 d t) (sns3 d t0))).(let H2 \def 
-H1 in (and_ind (sn3 d t) (sns3 d t0) (land (sn3 c (lift h i t)) (sns3 c 
+H1 in (land_ind (sn3 d t) (sns3 d t0) (land (sn3 c (lift h i t)) (sns3 c 
 (lifts h i t0))) (\lambda (H3: (sn3 d t)).(\lambda (H4: (sns3 d t0)).(conj 
 (sn3 c (lift h i t)) (sns3 c (lifts h i t0)) (sn3_lift d t H3 c h i H) (H0 
 H4)))) H2)))))) ts)))))).