X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1%2Fiso%2Ffwd.ma;h=fc3550a4cfd3602cfb9eedb6ada3e94556b425d6;hb=b4283c079ed7069016b8d924bbc7e08872440829;hp=761e982f7c40dd43a1534c3fd26b18113ead60a4;hpb=88a68a9c334646bc17314d5327cd3b790202acd6;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_1/iso/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1/iso/fwd.ma
index 761e982f7..fc3550a4c 100644
--- a/matita/matita/contribs/lambdadelta/basic_1/iso/fwd.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/iso/fwd.ma
@@ -14,11 +14,28 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/iso/defs.ma".
+include "basic_1/iso/defs.ma".
 
-include "Basic-1/tlist/defs.ma".
+include "basic_1/tlist/defs.ma".
 
-theorem iso_gen_sort:
+implied lemma iso_ind:
+ \forall (P: ((T \to (T \to Prop)))).(((\forall (n1: nat).(\forall (n2: 
+nat).(P (TSort n1) (TSort n2))))) \to (((\forall (i1: nat).(\forall (i2: 
+nat).(P (TLRef i1) (TLRef i2))))) \to (((\forall (v1: T).(\forall (v2: 
+T).(\forall (t1: T).(\forall (t2: T).(\forall (k: K).(P (THead k v1 t1) 
+(THead k v2 t2)))))))) \to (\forall (t: T).(\forall (t0: T).((iso t t0) \to 
+(P t t0)))))))
+\def
+ \lambda (P: ((T \to (T \to Prop)))).(\lambda (f: ((\forall (n1: 
+nat).(\forall (n2: nat).(P (TSort n1) (TSort n2)))))).(\lambda (f0: ((\forall 
+(i1: nat).(\forall (i2: nat).(P (TLRef i1) (TLRef i2)))))).(\lambda (f1: 
+((\forall (v1: T).(\forall (v2: T).(\forall (t1: T).(\forall (t2: T).(\forall 
+(k: K).(P (THead k v1 t1) (THead k v2 t2))))))))).(\lambda (t: T).(\lambda 
+(t0: T).(\lambda (i: (iso t t0)).(match i with [(iso_sort x x0) \Rightarrow 
+(f x x0) | (iso_lref x x0) \Rightarrow (f0 x x0) | (iso_head x x0 x1 x2 x3) 
+\Rightarrow (f1 x x0 x1 x2 x3)]))))))).
+
+lemma iso_gen_sort:
  \forall (u2: T).(\forall (n1: nat).((iso (TSort n1) u2) \to (ex nat (\lambda 
 (n2: nat).(eq T u2 (TSort n2))))))
 \def
@@ -28,26 +45,22 @@ nat (\lambda (n2: nat).(eq T u2 (TSort n2))))) (\lambda (y: T).(\lambda (H0:
 (iso y u2)).(iso_ind (\lambda (t: T).(\lambda (t0: T).((eq T t (TSort n1)) 
 \to (ex nat (\lambda (n2: nat).(eq T t0 (TSort n2))))))) (\lambda (n0: 
 nat).(\lambda (n2: nat).(\lambda (H1: (eq T (TSort n0) (TSort n1))).(let H2 
-\def (f_equal T nat (\lambda (e: T).(match e in T return (\lambda (_: T).nat) 
-with [(TSort n) \Rightarrow n | (TLRef _) \Rightarrow n0 | (THead _ _ _) 
-\Rightarrow n0])) (TSort n0) (TSort n1) H1) in (ex_intro nat (\lambda (n3: 
-nat).(eq T (TSort n2) (TSort n3))) n2 (refl_equal T (TSort n2))))))) (\lambda 
-(i1: nat).(\lambda (i2: nat).(\lambda (H1: (eq T (TLRef i1) (TSort n1))).(let 
-H2 \def (eq_ind T (TLRef i1) (\lambda (ee: T).(match ee in T return (\lambda 
-(_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True | 
-(THead _ _ _) \Rightarrow False])) I (TSort n1) H1) in (False_ind (ex nat 
-(\lambda (n2: nat).(eq T (TLRef i2) (TSort n2)))) H2))))) (\lambda (v1: 
+\def (f_equal T nat (\lambda (e: T).(match e with [(TSort n) \Rightarrow n | 
+(TLRef _) \Rightarrow n0 | (THead _ _ _) \Rightarrow n0])) (TSort n0) (TSort 
+n1) H1) in (ex_intro nat (\lambda (n3: nat).(eq T (TSort n2) (TSort n3))) n2 
+(refl_equal T (TSort n2))))))) (\lambda (i1: nat).(\lambda (i2: nat).(\lambda 
+(H1: (eq T (TLRef i1) (TSort n1))).(let H2 \def (eq_ind T (TLRef i1) (\lambda 
+(ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow 
+True | (THead _ _ _) \Rightarrow False])) I (TSort n1) H1) in (False_ind (ex 
+nat (\lambda (n2: nat).(eq T (TLRef i2) (TSort n2)))) H2))))) (\lambda (v1: 
 T).(\lambda (v2: T).(\lambda (t1: T).(\lambda (t2: T).(\lambda (k: 
 K).(\lambda (H1: (eq T (THead k v1 t1) (TSort n1))).(let H2 \def (eq_ind T 
-(THead k v1 t1) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) 
-with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ 
-_) \Rightarrow True])) I (TSort n1) H1) in (False_ind (ex nat (\lambda (n2: 
-nat).(eq T (THead k v2 t2) (TSort n2)))) H2)))))))) y u2 H0))) H))).
-(* COMMENTS
-Initial nodes: 321
-END *)
+(THead k v1 t1) (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False 
+| (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TSort 
+n1) H1) in (False_ind (ex nat (\lambda (n2: nat).(eq T (THead k v2 t2) (TSort 
+n2)))) H2)))))))) y u2 H0))) H))).
 
-theorem iso_gen_lref:
+lemma iso_gen_lref:
  \forall (u2: T).(\forall (n1: nat).((iso (TLRef n1) u2) \to (ex nat (\lambda 
 (n2: nat).(eq T u2 (TLRef n2))))))
 \def
@@ -57,26 +70,22 @@ nat (\lambda (n2: nat).(eq T u2 (TLRef n2))))) (\lambda (y: T).(\lambda (H0:
 (iso y u2)).(iso_ind (\lambda (t: T).(\lambda (t0: T).((eq T t (TLRef n1)) 
 \to (ex nat (\lambda (n2: nat).(eq T t0 (TLRef n2))))))) (\lambda (n0: 
 nat).(\lambda (n2: nat).(\lambda (H1: (eq T (TSort n0) (TLRef n1))).(let H2 
-\def (eq_ind T (TSort n0) (\lambda (ee: T).(match ee in T return (\lambda (_: 
-T).Prop) with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False | 
-(THead _ _ _) \Rightarrow False])) I (TLRef n1) H1) in (False_ind (ex nat 
-(\lambda (n3: nat).(eq T (TSort n2) (TLRef n3)))) H2))))) (\lambda (i1: 
-nat).(\lambda (i2: nat).(\lambda (H1: (eq T (TLRef i1) (TLRef n1))).(let H2 
-\def (f_equal T nat (\lambda (e: T).(match e in T return (\lambda (_: T).nat) 
-with [(TSort _) \Rightarrow i1 | (TLRef n) \Rightarrow n | (THead _ _ _) 
-\Rightarrow i1])) (TLRef i1) (TLRef n1) H1) in (ex_intro nat (\lambda (n2: 
-nat).(eq T (TLRef i2) (TLRef n2))) i2 (refl_equal T (TLRef i2))))))) (\lambda 
-(v1: T).(\lambda (v2: T).(\lambda (t1: T).(\lambda (t2: T).(\lambda (k: 
-K).(\lambda (H1: (eq T (THead k v1 t1) (TLRef n1))).(let H2 \def (eq_ind T 
-(THead k v1 t1) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) 
-with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ 
-_) \Rightarrow True])) I (TLRef n1) H1) in (False_ind (ex nat (\lambda (n2: 
+\def (eq_ind T (TSort n0) (\lambda (ee: T).(match ee with [(TSort _) 
+\Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow 
+False])) I (TLRef n1) H1) in (False_ind (ex nat (\lambda (n3: nat).(eq T 
+(TSort n2) (TLRef n3)))) H2))))) (\lambda (i1: nat).(\lambda (i2: 
+nat).(\lambda (H1: (eq T (TLRef i1) (TLRef n1))).(let H2 \def (f_equal T nat 
+(\lambda (e: T).(match e with [(TSort _) \Rightarrow i1 | (TLRef n) 
+\Rightarrow n | (THead _ _ _) \Rightarrow i1])) (TLRef i1) (TLRef n1) H1) in 
+(ex_intro nat (\lambda (n2: nat).(eq T (TLRef i2) (TLRef n2))) i2 (refl_equal 
+T (TLRef i2))))))) (\lambda (v1: T).(\lambda (v2: T).(\lambda (t1: 
+T).(\lambda (t2: T).(\lambda (k: K).(\lambda (H1: (eq T (THead k v1 t1) 
+(TLRef n1))).(let H2 \def (eq_ind T (THead k v1 t1) (\lambda (ee: T).(match 
+ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ 
+_ _) \Rightarrow True])) I (TLRef n1) H1) in (False_ind (ex nat (\lambda (n2: 
 nat).(eq T (THead k v2 t2) (TLRef n2)))) H2)))))))) y u2 H0))) H))).
-(* COMMENTS
-Initial nodes: 321
-END *)
 
-theorem iso_gen_head:
+lemma iso_gen_head:
  \forall (k: K).(\forall (v1: T).(\forall (t1: T).(\forall (u2: T).((iso 
 (THead k v1 t1) u2) \to (ex_2 T T (\lambda (v2: T).(\lambda (t2: T).(eq T u2 
 (THead k v2 t2)))))))))
@@ -88,37 +97,31 @@ T).(eq T u2 (THead k v2 t2)))))) (\lambda (y: T).(\lambda (H0: (iso y
 u2)).(iso_ind (\lambda (t: T).(\lambda (t0: T).((eq T t (THead k v1 t1)) \to 
 (ex_2 T T (\lambda (v2: T).(\lambda (t2: T).(eq T t0 (THead k v2 t2)))))))) 
 (\lambda (n1: nat).(\lambda (n2: nat).(\lambda (H1: (eq T (TSort n1) (THead k 
-v1 t1))).(let H2 \def (eq_ind T (TSort n1) (\lambda (ee: T).(match ee in T 
-return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow True | (TLRef _) 
-\Rightarrow False | (THead _ _ _) \Rightarrow False])) I (THead k v1 t1) H1) 
-in (False_ind (ex_2 T T (\lambda (v2: T).(\lambda (t2: T).(eq T (TSort n2) 
-(THead k v2 t2))))) H2))))) (\lambda (i1: nat).(\lambda (i2: nat).(\lambda 
-(H1: (eq T (TLRef i1) (THead k v1 t1))).(let H2 \def (eq_ind T (TLRef i1) 
-(\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _) 
-\Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow 
-False])) I (THead k v1 t1) H1) in (False_ind (ex_2 T T (\lambda (v2: 
-T).(\lambda (t2: T).(eq T (TLRef i2) (THead k v2 t2))))) H2))))) (\lambda 
-(v0: T).(\lambda (v2: T).(\lambda (t0: T).(\lambda (t2: T).(\lambda (k0: 
-K).(\lambda (H1: (eq T (THead k0 v0 t0) (THead k v1 t1))).(let H2 \def 
-(f_equal T K (\lambda (e: T).(match e in T return (\lambda (_: T).K) with 
-[(TSort _) \Rightarrow k0 | (TLRef _) \Rightarrow k0 | (THead k1 _ _) 
-\Rightarrow k1])) (THead k0 v0 t0) (THead k v1 t1) H1) in ((let H3 \def 
-(f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with 
+v1 t1))).(let H2 \def (eq_ind T (TSort n1) (\lambda (ee: T).(match ee with 
+[(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) 
+\Rightarrow False])) I (THead k v1 t1) H1) in (False_ind (ex_2 T T (\lambda 
+(v2: T).(\lambda (t2: T).(eq T (TSort n2) (THead k v2 t2))))) H2))))) 
+(\lambda (i1: nat).(\lambda (i2: nat).(\lambda (H1: (eq T (TLRef i1) (THead k 
+v1 t1))).(let H2 \def (eq_ind T (TLRef i1) (\lambda (ee: T).(match ee with 
+[(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _) 
+\Rightarrow False])) I (THead k v1 t1) H1) in (False_ind (ex_2 T T (\lambda 
+(v2: T).(\lambda (t2: T).(eq T (TLRef i2) (THead k v2 t2))))) H2))))) 
+(\lambda (v0: T).(\lambda (v2: T).(\lambda (t0: T).(\lambda (t2: T).(\lambda 
+(k0: K).(\lambda (H1: (eq T (THead k0 v0 t0) (THead k v1 t1))).(let H2 \def 
+(f_equal T K (\lambda (e: T).(match e with [(TSort _) \Rightarrow k0 | (TLRef 
+_) \Rightarrow k0 | (THead k1 _ _) \Rightarrow k1])) (THead k0 v0 t0) (THead 
+k v1 t1) H1) in ((let H3 \def (f_equal T T (\lambda (e: T).(match e with 
 [(TSort _) \Rightarrow v0 | (TLRef _) \Rightarrow v0 | (THead _ t _) 
 \Rightarrow t])) (THead k0 v0 t0) (THead k v1 t1) H1) in ((let H4 \def 
-(f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with 
-[(TSort _) \Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t) 
-\Rightarrow t])) (THead k0 v0 t0) (THead k v1 t1) H1) in (\lambda (_: (eq T 
-v0 v1)).(\lambda (H6: (eq K k0 k)).(eq_ind_r K k (\lambda (k1: K).(ex_2 T T 
-(\lambda (v3: T).(\lambda (t3: T).(eq T (THead k1 v2 t2) (THead k v3 t3)))))) 
-(ex_2_intro T T (\lambda (v3: T).(\lambda (t3: T).(eq T (THead k v2 t2) 
-(THead k v3 t3)))) v2 t2 (refl_equal T (THead k v2 t2))) k0 H6)))) H3)) 
-H2)))))))) y u2 H0))) H))))).
-(* COMMENTS
-Initial nodes: 545
-END *)
+(f_equal T T (\lambda (e: T).(match e with [(TSort _) \Rightarrow t0 | (TLRef 
+_) \Rightarrow t0 | (THead _ _ t) \Rightarrow t])) (THead k0 v0 t0) (THead k 
+v1 t1) H1) in (\lambda (_: (eq T v0 v1)).(\lambda (H6: (eq K k0 k)).(eq_ind_r 
+K k (\lambda (k1: K).(ex_2 T T (\lambda (v3: T).(\lambda (t3: T).(eq T (THead 
+k1 v2 t2) (THead k v3 t3)))))) (ex_2_intro T T (\lambda (v3: T).(\lambda (t3: 
+T).(eq T (THead k v2 t2) (THead k v3 t3)))) v2 t2 (refl_equal T (THead k v2 
+t2))) k0 H6)))) H3)) H2)))))))) y u2 H0))) H))))).
 
-theorem iso_flats_lref_bind_false:
+lemma iso_flats_lref_bind_false:
  \forall (f: F).(\forall (b: B).(\forall (i: nat).(\forall (v: T).(\forall 
 (t: T).(\forall (vs: TList).((iso (THeads (Flat f) vs (TLRef i)) (THead (Bind 
 b) v t)) \to (\forall (P: Prop).P)))))))
@@ -130,28 +133,23 @@ b) v t)) \to (\forall (P: Prop).P)))))))
 H_x \def (iso_gen_lref (THead (Bind b) v t) i H) in (let H0 \def H_x in 
 (ex_ind nat (\lambda (n2: nat).(eq T (THead (Bind b) v t) (TLRef n2))) P 
 (\lambda (x: nat).(\lambda (H1: (eq T (THead (Bind b) v t) (TLRef x))).(let 
-H2 \def (eq_ind T (THead (Bind b) v t) (\lambda (ee: T).(match ee in T return 
-(\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) 
-\Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TLRef x) H1) in 
-(False_ind P H2)))) H0))))) (\lambda (t0: T).(\lambda (t1: TList).(\lambda 
-(_: (((iso (THeads (Flat f) t1 (TLRef i)) (THead (Bind b) v t)) \to (\forall 
-(P: Prop).P)))).(\lambda (H0: (iso (THead (Flat f) t0 (THeads (Flat f) t1 
-(TLRef i))) (THead (Bind b) v t))).(\lambda (P: Prop).(let H_x \def 
-(iso_gen_head (Flat f) t0 (THeads (Flat f) t1 (TLRef i)) (THead (Bind b) v t) 
-H0) in (let H1 \def H_x in (ex_2_ind T T (\lambda (v2: T).(\lambda (t2: 
-T).(eq T (THead (Bind b) v t) (THead (Flat f) v2 t2)))) P (\lambda (x0: 
-T).(\lambda (x1: T).(\lambda (H2: (eq T (THead (Bind b) v t) (THead (Flat f) 
-x0 x1))).(let H3 \def (eq_ind T (THead (Bind b) v t) (\lambda (ee: T).(match 
-ee in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | 
-(TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow (match k in K return 
-(\lambda (_: K).Prop) with [(Bind _) \Rightarrow True | (Flat _) \Rightarrow 
-False])])) I (THead (Flat f) x0 x1) H2) in (False_ind P H3))))) H1)))))))) 
-vs)))))).
-(* COMMENTS
-Initial nodes: 391
-END *)
+H2 \def (eq_ind T (THead (Bind b) v t) (\lambda (ee: T).(match ee with 
+[(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _) 
+\Rightarrow True])) I (TLRef x) H1) in (False_ind P H2)))) H0))))) (\lambda 
+(t0: T).(\lambda (t1: TList).(\lambda (_: (((iso (THeads (Flat f) t1 (TLRef 
+i)) (THead (Bind b) v t)) \to (\forall (P: Prop).P)))).(\lambda (H0: (iso 
+(THead (Flat f) t0 (THeads (Flat f) t1 (TLRef i))) (THead (Bind b) v 
+t))).(\lambda (P: Prop).(let H_x \def (iso_gen_head (Flat f) t0 (THeads (Flat 
+f) t1 (TLRef i)) (THead (Bind b) v t) H0) in (let H1 \def H_x in (ex_2_ind T 
+T (\lambda (v2: T).(\lambda (t2: T).(eq T (THead (Bind b) v t) (THead (Flat 
+f) v2 t2)))) P (\lambda (x0: T).(\lambda (x1: T).(\lambda (H2: (eq T (THead 
+(Bind b) v t) (THead (Flat f) x0 x1))).(let H3 \def (eq_ind T (THead (Bind b) 
+v t) (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) 
+\Rightarrow False | (THead k _ _) \Rightarrow (match k with [(Bind _) 
+\Rightarrow True | (Flat _) \Rightarrow False])])) I (THead (Flat f) x0 x1) 
+H2) in (False_ind P H3))))) H1)))))))) vs)))))).
 
-theorem iso_flats_flat_bind_false:
+lemma iso_flats_flat_bind_false:
  \forall (f1: F).(\forall (f2: F).(\forall (b: B).(\forall (v: T).(\forall 
 (v2: T).(\forall (t: T).(\forall (t2: T).(\forall (vs: TList).((iso (THeads 
 (Flat f1) vs (THead (Flat f2) v2 t2)) (THead (Bind b) v t)) \to (\forall (P: 
@@ -166,9 +164,8 @@ Prop).P)))))))))
 (ex_2_ind T T (\lambda (v3: T).(\lambda (t3: T).(eq T (THead (Bind b) v t) 
 (THead (Flat f2) v3 t3)))) P (\lambda (x0: T).(\lambda (x1: T).(\lambda (H1: 
 (eq T (THead (Bind b) v t) (THead (Flat f2) x0 x1))).(let H2 \def (eq_ind T 
-(THead (Bind b) v t) (\lambda (ee: T).(match ee in T return (\lambda (_: 
-T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | 
-(THead k _ _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with 
+(THead (Bind b) v t) (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow 
+False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow (match k with 
 [(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])])) I (THead (Flat 
 f2) x0 x1) H1) in (False_ind P H2))))) H0))))) (\lambda (t0: T).(\lambda (t1: 
 TList).(\lambda (_: (((iso (THeads (Flat f1) t1 (THead (Flat f2) v2 t2)) 
@@ -179,13 +176,9 @@ t))).(\lambda (P: Prop).(let H_x \def (iso_gen_head (Flat f1) t0 (THeads
 \def H_x in (ex_2_ind T T (\lambda (v3: T).(\lambda (t3: T).(eq T (THead 
 (Bind b) v t) (THead (Flat f1) v3 t3)))) P (\lambda (x0: T).(\lambda (x1: 
 T).(\lambda (H2: (eq T (THead (Bind b) v t) (THead (Flat f1) x0 x1))).(let H3 
-\def (eq_ind T (THead (Bind b) v t) (\lambda (ee: T).(match ee in T return 
-(\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) 
-\Rightarrow False | (THead k _ _) \Rightarrow (match k in K return (\lambda 
-(_: K).Prop) with [(Bind _) \Rightarrow True | (Flat _) \Rightarrow 
+\def (eq_ind T (THead (Bind b) v t) (\lambda (ee: T).(match ee with [(TSort 
+_) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _) 
+\Rightarrow (match k with [(Bind _) \Rightarrow True | (Flat _) \Rightarrow 
 False])])) I (THead (Flat f1) x0 x1) H2) in (False_ind P H3))))) H1)))))))) 
 vs)))))))).
-(* COMMENTS
-Initial nodes: 461
-END *)