X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1%2Fty3%2Ffwd_nf2.ma;h=d98b4020c16547fd3899c9bbf0db9c1f13b9d499;hb=a04fa03fcea0493e89b725960146cc0c06539583;hp=ca4e40c7bbf2a25dd4814949042fcc8eb2f90eb8;hpb=88a68a9c334646bc17314d5327cd3b790202acd6;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_1/ty3/fwd_nf2.ma b/matita/matita/contribs/lambdadelta/basic_1/ty3/fwd_nf2.ma
index ca4e40c7b..d98b4020c 100644
--- a/matita/matita/contribs/lambdadelta/basic_1/ty3/fwd_nf2.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/ty3/fwd_nf2.ma
@@ -14,13 +14,13 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/ty3/arity_props.ma".
+include "basic_1/ty3/arity_props.ma".
 
-include "Basic-1/pc3/nf2.ma".
+include "basic_1/pc3/nf2.ma".
 
-include "Basic-1/nf2/fwd.ma".
+include "basic_1/nf2/fwd.ma".
 
-theorem ty3_gen_appl_nf2:
+lemma ty3_gen_appl_nf2:
  \forall (g: G).(\forall (c: C).(\forall (w: T).(\forall (v: T).(\forall (x: 
 T).((ty3 g c (THead (Flat Appl) w v) x) \to (ex4_2 T T (\lambda (u: 
 T).(\lambda (t: T).(pc3 c (THead (Flat Appl) w (THead (Bind Abst) u t)) x))) 
@@ -85,11 +85,8 @@ Abst) x0 x1) H1 (pc3_pr3_r c (THead (Bind Abst) x0 x1) (THead (Bind Abst) x5
 x6) H16)) (ty3_conv g c x5 x3 (ty3_sred_pr3 c x0 x5 H13 g x3 H6) w x0 H2 
 (pc3_pr3_r c x0 x5 H13)) H15)))))))) H11))))) H8)))))) H5))))) H3)))))))) 
 (ty3_gen_appl g c w v x H))))))).
-(* COMMENTS
-Initial nodes: 1289
-END *)
 
-theorem ty3_inv_lref_nf2_pc3:
+lemma ty3_inv_lref_nf2_pc3:
  \forall (g: G).(\forall (c: C).(\forall (u1: T).(\forall (i: nat).((ty3 g c 
 (TLRef i) u1) \to ((nf2 c (TLRef i)) \to (\forall (u2: T).((nf2 c u2) \to 
 ((pc3 c u1 u2) \to (ex T (\lambda (u: T).(eq T u2 (lift (S i) O u))))))))))))
@@ -119,19 +116,18 @@ T).(eq T u3 (lift (S i) O u0)))))))))) H4 (TLRef i) H6) in (let H12 \def
 H9))))))))))))))))))))) (\lambda (c0: C).(\lambda (m: nat).(\lambda (H1: (eq 
 T (TSort m) (TLRef i))).(\lambda (_: (nf2 c0 (TSort m))).(\lambda (u2: 
 T).(\lambda (_: (nf2 c0 u2)).(\lambda (_: (pc3 c0 (TSort (next g m)) 
-u2)).(let H5 \def (eq_ind T (TSort m) (\lambda (ee: T).(match ee in T return 
-(\lambda (_: T).Prop) with [(TSort _) \Rightarrow True | (TLRef _) 
-\Rightarrow False | (THead _ _ _) \Rightarrow False])) I (TLRef i) H1) in 
-(False_ind (ex T (\lambda (u: T).(eq T u2 (lift (S i) O u)))) H5))))))))) 
-(\lambda (n: nat).(\lambda (c0: C).(\lambda (d: C).(\lambda (u: T).(\lambda 
-(H1: (getl n c0 (CHead d (Bind Abbr) u))).(\lambda (t: T).(\lambda (_: (ty3 g 
-d u t)).(\lambda (_: (((eq T u (TLRef i)) \to ((nf2 d u) \to (\forall (u2: 
-T).((nf2 d u2) \to ((pc3 d t u2) \to (ex T (\lambda (u0: T).(eq T u2 (lift (S 
-i) O u0))))))))))).(\lambda (H4: (eq T (TLRef n) (TLRef i))).(\lambda (H5: 
-(nf2 c0 (TLRef n))).(\lambda (u2: T).(\lambda (_: (nf2 c0 u2)).(\lambda (H7: 
-(pc3 c0 (lift (S n) O t) u2)).(let H8 \def (f_equal T nat (\lambda (e: 
-T).(match e in T return (\lambda (_: T).nat) with [(TSort _) \Rightarrow n | 
-(TLRef n0) \Rightarrow n0 | (THead _ _ _) \Rightarrow n])) (TLRef n) (TLRef 
+u2)).(let H5 \def (eq_ind T (TSort m) (\lambda (ee: T).(match ee with [(TSort 
+_) \Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow 
+False])) I (TLRef i) H1) in (False_ind (ex T (\lambda (u: T).(eq T u2 (lift 
+(S i) O u)))) H5))))))))) (\lambda (n: nat).(\lambda (c0: C).(\lambda (d: 
+C).(\lambda (u: T).(\lambda (H1: (getl n c0 (CHead d (Bind Abbr) 
+u))).(\lambda (t: T).(\lambda (_: (ty3 g d u t)).(\lambda (_: (((eq T u 
+(TLRef i)) \to ((nf2 d u) \to (\forall (u2: T).((nf2 d u2) \to ((pc3 d t u2) 
+\to (ex T (\lambda (u0: T).(eq T u2 (lift (S i) O u0))))))))))).(\lambda (H4: 
+(eq T (TLRef n) (TLRef i))).(\lambda (H5: (nf2 c0 (TLRef n))).(\lambda (u2: 
+T).(\lambda (_: (nf2 c0 u2)).(\lambda (H7: (pc3 c0 (lift (S n) O t) u2)).(let 
+H8 \def (f_equal T nat (\lambda (e: T).(match e with [(TSort _) \Rightarrow n 
+| (TLRef n0) \Rightarrow n0 | (THead _ _ _) \Rightarrow n])) (TLRef n) (TLRef 
 i) H4) in (let H9 \def (eq_ind nat n (\lambda (n0: nat).(pc3 c0 (lift (S n0) 
 O t) u2)) H7 i H8) in (let H10 \def (eq_ind nat n (\lambda (n0: nat).(nf2 c0 
 (TLRef n0))) H5 i H8) in (let H11 \def (eq_ind nat n (\lambda (n0: nat).(getl 
@@ -144,66 +140,62 @@ T).((nf2 d u2) \to ((pc3 d t u2) \to (ex T (\lambda (u0: T).(eq T u2 (lift (S
 i) O u0))))))))))).(\lambda (H4: (eq T (TLRef n) (TLRef i))).(\lambda (H5: 
 (nf2 c0 (TLRef n))).(\lambda (u2: T).(\lambda (H6: (nf2 c0 u2)).(\lambda (H7: 
 (pc3 c0 (lift (S n) O u) u2)).(let H8 \def (f_equal T nat (\lambda (e: 
-T).(match e in T return (\lambda (_: T).nat) with [(TSort _) \Rightarrow n | 
-(TLRef n0) \Rightarrow n0 | (THead _ _ _) \Rightarrow n])) (TLRef n) (TLRef 
-i) H4) in (let H9 \def (eq_ind nat n (\lambda (n0: nat).(pc3 c0 (lift (S n0) 
-O u) u2)) H7 i H8) in (let H10 \def (eq_ind nat n (\lambda (n0: nat).(nf2 c0 
-(TLRef n0))) H5 i H8) in (let H11 \def (eq_ind nat n (\lambda (n0: nat).(getl 
-n0 c0 (CHead d (Bind Abst) u))) H1 i H8) in (let H_y \def (pc3_nf2_unfold c0 
-(lift (S i) O u) u2 H9 H6) in (let H12 \def (pr3_gen_lift c0 u u2 (S i) O H_y 
-d (getl_drop Abst c0 d u i H11)) in (ex2_ind T (\lambda (t2: T).(eq T u2 
-(lift (S i) O t2))) (\lambda (t2: T).(pr3 d u t2)) (ex T (\lambda (u0: T).(eq 
-T u2 (lift (S i) O u0)))) (\lambda (x: T).(\lambda (H13: (eq T u2 (lift (S i) 
-O x))).(\lambda (_: (pr3 d u x)).(eq_ind_r T (lift (S i) O x) (\lambda (t0: 
-T).(ex T (\lambda (u0: T).(eq T t0 (lift (S i) O u0))))) (ex_intro T (\lambda 
-(u0: T).(eq T (lift (S i) O x) (lift (S i) O u0))) x (refl_equal T (lift (S 
-i) O x))) u2 H13)))) H12)))))))))))))))))))) (\lambda (c0: C).(\lambda (u: 
-T).(\lambda (t: T).(\lambda (_: (ty3 g c0 u t)).(\lambda (_: (((eq T u (TLRef 
-i)) \to ((nf2 c0 u) \to (\forall (u2: T).((nf2 c0 u2) \to ((pc3 c0 t u2) \to 
-(ex T (\lambda (u0: T).(eq T u2 (lift (S i) O u0))))))))))).(\lambda (b: 
-B).(\lambda (t1: T).(\lambda (t2: T).(\lambda (_: (ty3 g (CHead c0 (Bind b) 
-u) t1 t2)).(\lambda (_: (((eq T t1 (TLRef i)) \to ((nf2 (CHead c0 (Bind b) u) 
-t1) \to (\forall (u2: T).((nf2 (CHead c0 (Bind b) u) u2) \to ((pc3 (CHead c0 
+T).(match e with [(TSort _) \Rightarrow n | (TLRef n0) \Rightarrow n0 | 
+(THead _ _ _) \Rightarrow n])) (TLRef n) (TLRef i) H4) in (let H9 \def 
+(eq_ind nat n (\lambda (n0: nat).(pc3 c0 (lift (S n0) O u) u2)) H7 i H8) in 
+(let H10 \def (eq_ind nat n (\lambda (n0: nat).(nf2 c0 (TLRef n0))) H5 i H8) 
+in (let H11 \def (eq_ind nat n (\lambda (n0: nat).(getl n0 c0 (CHead d (Bind 
+Abst) u))) H1 i H8) in (let H_y \def (pc3_nf2_unfold c0 (lift (S i) O u) u2 
+H9 H6) in (let H12 \def (pr3_gen_lift c0 u u2 (S i) O H_y d (getl_drop Abst 
+c0 d u i H11)) in (ex2_ind T (\lambda (t2: T).(eq T u2 (lift (S i) O t2))) 
+(\lambda (t2: T).(pr3 d u t2)) (ex T (\lambda (u0: T).(eq T u2 (lift (S i) O 
+u0)))) (\lambda (x: T).(\lambda (H13: (eq T u2 (lift (S i) O x))).(\lambda 
+(_: (pr3 d u x)).(eq_ind_r T (lift (S i) O x) (\lambda (t0: T).(ex T (\lambda 
+(u0: T).(eq T t0 (lift (S i) O u0))))) (ex_intro T (\lambda (u0: T).(eq T 
+(lift (S i) O x) (lift (S i) O u0))) x (refl_equal T (lift (S i) O x))) u2 
+H13)))) H12)))))))))))))))))))) (\lambda (c0: C).(\lambda (u: T).(\lambda (t: 
+T).(\lambda (_: (ty3 g c0 u t)).(\lambda (_: (((eq T u (TLRef i)) \to ((nf2 
+c0 u) \to (\forall (u2: T).((nf2 c0 u2) \to ((pc3 c0 t u2) \to (ex T (\lambda 
+(u0: T).(eq T u2 (lift (S i) O u0))))))))))).(\lambda (b: B).(\lambda (t1: 
+T).(\lambda (t2: T).(\lambda (_: (ty3 g (CHead c0 (Bind b) u) t1 
+t2)).(\lambda (_: (((eq T t1 (TLRef i)) \to ((nf2 (CHead c0 (Bind b) u) t1) 
+\to (\forall (u2: T).((nf2 (CHead c0 (Bind b) u) u2) \to ((pc3 (CHead c0 
 (Bind b) u) t2 u2) \to (ex T (\lambda (u0: T).(eq T u2 (lift (S i) O 
 u0))))))))))).(\lambda (H5: (eq T (THead (Bind b) u t1) (TLRef i))).(\lambda 
 (_: (nf2 c0 (THead (Bind b) u t1))).(\lambda (u2: T).(\lambda (_: (nf2 c0 
 u2)).(\lambda (_: (pc3 c0 (THead (Bind b) u t2) u2)).(let H9 \def (eq_ind T 
-(THead (Bind b) u t1) (\lambda (ee: T).(match ee in T return (\lambda (_: 
-T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | 
-(THead _ _ _) \Rightarrow True])) I (TLRef i) H5) in (False_ind (ex T 
-(\lambda (u0: T).(eq T u2 (lift (S i) O u0)))) H9))))))))))))))))) (\lambda 
-(c0: C).(\lambda (w: T).(\lambda (u: T).(\lambda (_: (ty3 g c0 w u)).(\lambda 
-(_: (((eq T w (TLRef i)) \to ((nf2 c0 w) \to (\forall (u2: T).((nf2 c0 u2) 
-\to ((pc3 c0 u u2) \to (ex T (\lambda (u0: T).(eq T u2 (lift (S i) O 
-u0))))))))))).(\lambda (v: T).(\lambda (t: T).(\lambda (_: (ty3 g c0 v (THead 
-(Bind Abst) u t))).(\lambda (_: (((eq T v (TLRef i)) \to ((nf2 c0 v) \to 
-(\forall (u2: T).((nf2 c0 u2) \to ((pc3 c0 (THead (Bind Abst) u t) u2) \to 
-(ex T (\lambda (u0: T).(eq T u2 (lift (S i) O u0))))))))))).(\lambda (H5: (eq 
-T (THead (Flat Appl) w v) (TLRef i))).(\lambda (_: (nf2 c0 (THead (Flat Appl) 
-w v))).(\lambda (u2: T).(\lambda (_: (nf2 c0 u2)).(\lambda (_: (pc3 c0 (THead 
-(Flat Appl) w (THead (Bind Abst) u t)) u2)).(let H9 \def (eq_ind T (THead 
-(Flat Appl) w v) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) 
-with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ 
-_) \Rightarrow True])) I (TLRef i) H5) in (False_ind (ex T (\lambda (u0: 
-T).(eq T u2 (lift (S i) O u0)))) H9)))))))))))))))) (\lambda (c0: C).(\lambda 
-(t1: T).(\lambda (t2: T).(\lambda (_: (ty3 g c0 t1 t2)).(\lambda (_: (((eq T 
-t1 (TLRef i)) \to ((nf2 c0 t1) \to (\forall (u2: T).((nf2 c0 u2) \to ((pc3 c0 
-t2 u2) \to (ex T (\lambda (u: T).(eq T u2 (lift (S i) O u))))))))))).(\lambda 
-(t0: T).(\lambda (_: (ty3 g c0 t2 t0)).(\lambda (_: (((eq T t2 (TLRef i)) \to 
-((nf2 c0 t2) \to (\forall (u2: T).((nf2 c0 u2) \to ((pc3 c0 t0 u2) \to (ex T 
-(\lambda (u: T).(eq T u2 (lift (S i) O u))))))))))).(\lambda (H5: (eq T 
-(THead (Flat Cast) t2 t1) (TLRef i))).(\lambda (_: (nf2 c0 (THead (Flat Cast) 
-t2 t1))).(\lambda (u2: T).(\lambda (_: (nf2 c0 u2)).(\lambda (_: (pc3 c0 
-(THead (Flat Cast) t0 t2) u2)).(let H9 \def (eq_ind T (THead (Flat Cast) t2 
-t1) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort 
-_) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _) 
-\Rightarrow True])) I (TLRef i) H5) in (False_ind (ex T (\lambda (u: T).(eq T 
-u2 (lift (S i) O u)))) H9))))))))))))))) c y u1 H0))) H))))).
-(* COMMENTS
-Initial nodes: 2175
-END *)
+(THead (Bind b) u t1) (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow 
+False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) I 
+(TLRef i) H5) in (False_ind (ex T (\lambda (u0: T).(eq T u2 (lift (S i) O 
+u0)))) H9))))))))))))))))) (\lambda (c0: C).(\lambda (w: T).(\lambda (u: 
+T).(\lambda (_: (ty3 g c0 w u)).(\lambda (_: (((eq T w (TLRef i)) \to ((nf2 
+c0 w) \to (\forall (u2: T).((nf2 c0 u2) \to ((pc3 c0 u u2) \to (ex T (\lambda 
+(u0: T).(eq T u2 (lift (S i) O u0))))))))))).(\lambda (v: T).(\lambda (t: 
+T).(\lambda (_: (ty3 g c0 v (THead (Bind Abst) u t))).(\lambda (_: (((eq T v 
+(TLRef i)) \to ((nf2 c0 v) \to (\forall (u2: T).((nf2 c0 u2) \to ((pc3 c0 
+(THead (Bind Abst) u t) u2) \to (ex T (\lambda (u0: T).(eq T u2 (lift (S i) O 
+u0))))))))))).(\lambda (H5: (eq T (THead (Flat Appl) w v) (TLRef 
+i))).(\lambda (_: (nf2 c0 (THead (Flat Appl) w v))).(\lambda (u2: T).(\lambda 
+(_: (nf2 c0 u2)).(\lambda (_: (pc3 c0 (THead (Flat Appl) w (THead (Bind Abst) 
+u t)) u2)).(let H9 \def (eq_ind T (THead (Flat Appl) w v) (\lambda (ee: 
+T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False 
+| (THead _ _ _) \Rightarrow True])) I (TLRef i) H5) in (False_ind (ex T 
+(\lambda (u0: T).(eq T u2 (lift (S i) O u0)))) H9)))))))))))))))) (\lambda 
+(c0: C).(\lambda (t1: T).(\lambda (t2: T).(\lambda (_: (ty3 g c0 t1 
+t2)).(\lambda (_: (((eq T t1 (TLRef i)) \to ((nf2 c0 t1) \to (\forall (u2: 
+T).((nf2 c0 u2) \to ((pc3 c0 t2 u2) \to (ex T (\lambda (u: T).(eq T u2 (lift 
+(S i) O u))))))))))).(\lambda (t0: T).(\lambda (_: (ty3 g c0 t2 t0)).(\lambda 
+(_: (((eq T t2 (TLRef i)) \to ((nf2 c0 t2) \to (\forall (u2: T).((nf2 c0 u2) 
+\to ((pc3 c0 t0 u2) \to (ex T (\lambda (u: T).(eq T u2 (lift (S i) O 
+u))))))))))).(\lambda (H5: (eq T (THead (Flat Cast) t2 t1) (TLRef 
+i))).(\lambda (_: (nf2 c0 (THead (Flat Cast) t2 t1))).(\lambda (u2: 
+T).(\lambda (_: (nf2 c0 u2)).(\lambda (_: (pc3 c0 (THead (Flat Cast) t0 t2) 
+u2)).(let H9 \def (eq_ind T (THead (Flat Cast) t2 t1) (\lambda (ee: T).(match 
+ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ 
+_ _) \Rightarrow True])) I (TLRef i) H5) in (False_ind (ex T (\lambda (u: 
+T).(eq T u2 (lift (S i) O u)))) H9))))))))))))))) c y u1 H0))) H))))).
 
-theorem ty3_inv_lref_nf2:
+lemma ty3_inv_lref_nf2:
  \forall (g: G).(\forall (c: C).(\forall (u: T).(\forall (i: nat).((ty3 g c 
 (TLRef i) u) \to ((nf2 c (TLRef i)) \to ((nf2 c u) \to (ex T (\lambda (u0: 
 T).(eq T u (lift (S i) O u0))))))))))
@@ -211,11 +203,8 @@ T).(eq T u (lift (S i) O u0))))))))))
  \lambda (g: G).(\lambda (c: C).(\lambda (u: T).(\lambda (i: nat).(\lambda 
 (H: (ty3 g c (TLRef i) u)).(\lambda (H0: (nf2 c (TLRef i))).(\lambda (H1: 
 (nf2 c u)).(ty3_inv_lref_nf2_pc3 g c u i H H0 u H1 (pc3_refl c u)))))))).
-(* COMMENTS
-Initial nodes: 57
-END *)
 
-theorem ty3_inv_appls_lref_nf2:
+lemma ty3_inv_appls_lref_nf2:
  \forall (g: G).(\forall (c: C).(\forall (vs: TList).(\forall (u1: 
 T).(\forall (i: nat).((ty3 g c (THeads (Flat Appl) vs (TLRef i)) u1) \to 
 ((nf2 c (TLRef i)) \to ((nf2 c u1) \to (ex2 T (\lambda (u: T).(nf2 c (lift (S 
@@ -272,11 +261,8 @@ i) O u))) u1)) x H12 (pc3_t (THead (Flat Appl) t (THead (Bind Abst) x0 x1)) c
 (THead (Flat Appl) t (THeads (Flat Appl) t0 (lift (S i) O x))) (pc3_thin_dx c 
 (THeads (Flat Appl) t0 (lift (S i) O x)) (THead (Bind Abst) x0 x1) H13 t 
 Appl) u1 H4))))) H11))))) H8)))))))) H3))))))))))) vs))).
-(* COMMENTS
-Initial nodes: 1213
-END *)
 
-theorem ty3_inv_lref_lref_nf2:
+lemma ty3_inv_lref_lref_nf2:
  \forall (g: G).(\forall (c: C).(\forall (i: nat).(\forall (j: nat).((ty3 g c 
 (TLRef i) (TLRef j)) \to ((nf2 c (TLRef i)) \to ((nf2 c (TLRef j)) \to (lt i 
 j)))))))
@@ -295,7 +281,4 @@ j O)).(\lambda (_: (eq T x (TLRef j))).(lt_x_O j H6 (lt i j)))) H5)) (\lambda
 i) j) (eq T x (TLRef (minus j (S i)))) (lt i j) (\lambda (H6: (le (S i) 
 j)).(\lambda (_: (eq T x (TLRef (minus j (S i))))).H6)) H5)) H4))))) 
 H2))))))))).
-(* COMMENTS
-Initial nodes: 337
-END *)