X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matitaB%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FBasic-1%2Fclear%2Ffwd.ma;fp=matitaB%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FBasic-1%2Fclear%2Ffwd.ma;h=0000000000000000000000000000000000000000;hb=88a68a9c334646bc17314d5327cd3b790202acd6;hp=d64ff77becc37bfac84d3889f01ebf257c4457cf;hpb=4904accd80118cb8126e308ae098d87f8651c9f4;p=helm.git

diff --git a/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/clear/fwd.ma b/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/clear/fwd.ma
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-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-(* This file was automatically generated: do not edit *********************)
-
-include "Basic-1/clear/defs.ma".
-
-theorem clear_gen_sort:
- \forall (x: C).(\forall (n: nat).((clear (CSort n) x) \to (\forall (P: 
-Prop).P)))
-\def
- \lambda (x: C).(\lambda (n: nat).(\lambda (H: (clear (CSort n) x)).(\lambda 
-(P: Prop).(insert_eq C (CSort n) (\lambda (c: C).(clear c x)) (\lambda (_: 
-C).P) (\lambda (y: C).(\lambda (H0: (clear y x)).(clear_ind (\lambda (c: 
-C).(\lambda (_: C).((eq C c (CSort n)) \to P))) (\lambda (b: B).(\lambda (e: 
-C).(\lambda (u: T).(\lambda (H1: (eq C (CHead e (Bind b) u) (CSort n))).(let 
-H2 \def (eq_ind C (CHead e (Bind b) u) (\lambda (ee: C).(match ee in C return 
-(\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | (CHead _ _ _) 
-\Rightarrow True])) I (CSort n) H1) in (False_ind P H2)))))) (\lambda (e: 
-C).(\lambda (c: C).(\lambda (_: (clear e c)).(\lambda (_: (((eq C e (CSort 
-n)) \to P))).(\lambda (f: F).(\lambda (u: T).(\lambda (H3: (eq C (CHead e 
-(Flat f) u) (CSort n))).(let H4 \def (eq_ind C (CHead e (Flat f) u) (\lambda 
-(ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _) 
-\Rightarrow False | (CHead _ _ _) \Rightarrow True])) I (CSort n) H3) in 
-(False_ind P H4))))))))) y x H0))) H)))).
-(* COMMENTS
-Initial nodes: 215
-END *)
-
-theorem clear_gen_bind:
- \forall (b: B).(\forall (e: C).(\forall (x: C).(\forall (u: T).((clear 
-(CHead e (Bind b) u) x) \to (eq C x (CHead e (Bind b) u))))))
-\def
- \lambda (b: B).(\lambda (e: C).(\lambda (x: C).(\lambda (u: T).(\lambda (H: 
-(clear (CHead e (Bind b) u) x)).(insert_eq C (CHead e (Bind b) u) (\lambda 
-(c: C).(clear c x)) (\lambda (c: C).(eq C x c)) (\lambda (y: C).(\lambda (H0: 
-(clear y x)).(clear_ind (\lambda (c: C).(\lambda (c0: C).((eq C c (CHead e 
-(Bind b) u)) \to (eq C c0 c)))) (\lambda (b0: B).(\lambda (e0: C).(\lambda 
-(u0: T).(\lambda (H1: (eq C (CHead e0 (Bind b0) u0) (CHead e (Bind b) 
-u))).(let H2 \def (f_equal C C (\lambda (e1: C).(match e1 in C return 
-(\lambda (_: C).C) with [(CSort _) \Rightarrow e0 | (CHead c _ _) \Rightarrow 
-c])) (CHead e0 (Bind b0) u0) (CHead e (Bind b) u) H1) in ((let H3 \def 
-(f_equal C B (\lambda (e1: C).(match e1 in C return (\lambda (_: C).B) with 
-[(CSort _) \Rightarrow b0 | (CHead _ k _) \Rightarrow (match k in K return 
-(\lambda (_: K).B) with [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow 
-b0])])) (CHead e0 (Bind b0) u0) (CHead e (Bind b) u) H1) in ((let H4 \def 
-(f_equal C T (\lambda (e1: C).(match e1 in C return (\lambda (_: C).T) with 
-[(CSort _) \Rightarrow u0 | (CHead _ _ t) \Rightarrow t])) (CHead e0 (Bind 
-b0) u0) (CHead e (Bind b) u) H1) in (\lambda (H5: (eq B b0 b)).(\lambda (H6: 
-(eq C e0 e)).(eq_ind_r T u (\lambda (t: T).(eq C (CHead e0 (Bind b0) t) 
-(CHead e0 (Bind b0) t))) (eq_ind_r C e (\lambda (c: C).(eq C (CHead c (Bind 
-b0) u) (CHead c (Bind b0) u))) (eq_ind_r B b (\lambda (b1: B).(eq C (CHead e 
-(Bind b1) u) (CHead e (Bind b1) u))) (refl_equal C (CHead e (Bind b) u)) b0 
-H5) e0 H6) u0 H4)))) H3)) H2)))))) (\lambda (e0: C).(\lambda (c: C).(\lambda 
-(_: (clear e0 c)).(\lambda (_: (((eq C e0 (CHead e (Bind b) u)) \to (eq C c 
-e0)))).(\lambda (f: F).(\lambda (u0: T).(\lambda (H3: (eq C (CHead e0 (Flat 
-f) u0) (CHead e (Bind b) u))).(let H4 \def (eq_ind C (CHead e0 (Flat f) u0) 
-(\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _) 
-\Rightarrow False | (CHead _ k _) \Rightarrow (match k in K return (\lambda 
-(_: K).Prop) with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow 
-True])])) I (CHead e (Bind b) u) H3) in (False_ind (eq C c (CHead e0 (Flat f) 
-u0)) H4))))))))) y x H0))) H))))).
-(* COMMENTS
-Initial nodes: 525
-END *)
-
-theorem clear_gen_flat:
- \forall (f: F).(\forall (e: C).(\forall (x: C).(\forall (u: T).((clear 
-(CHead e (Flat f) u) x) \to (clear e x)))))
-\def
- \lambda (f: F).(\lambda (e: C).(\lambda (x: C).(\lambda (u: T).(\lambda (H: 
-(clear (CHead e (Flat f) u) x)).(insert_eq C (CHead e (Flat f) u) (\lambda 
-(c: C).(clear c x)) (\lambda (_: C).(clear e x)) (\lambda (y: C).(\lambda 
-(H0: (clear y x)).(clear_ind (\lambda (c: C).(\lambda (c0: C).((eq C c (CHead 
-e (Flat f) u)) \to (clear e c0)))) (\lambda (b: B).(\lambda (e0: C).(\lambda 
-(u0: T).(\lambda (H1: (eq C (CHead e0 (Bind b) u0) (CHead e (Flat f) 
-u))).(let H2 \def (eq_ind C (CHead e0 (Bind b) u0) (\lambda (ee: C).(match ee 
-in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | (CHead 
-_ k _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind _) 
-\Rightarrow True | (Flat _) \Rightarrow False])])) I (CHead e (Flat f) u) H1) 
-in (False_ind (clear e (CHead e0 (Bind b) u0)) H2)))))) (\lambda (e0: 
-C).(\lambda (c: C).(\lambda (H1: (clear e0 c)).(\lambda (H2: (((eq C e0 
-(CHead e (Flat f) u)) \to (clear e c)))).(\lambda (f0: F).(\lambda (u0: 
-T).(\lambda (H3: (eq C (CHead e0 (Flat f0) u0) (CHead e (Flat f) u))).(let H4 
-\def (f_equal C C (\lambda (e1: C).(match e1 in C return (\lambda (_: C).C) 
-with [(CSort _) \Rightarrow e0 | (CHead c0 _ _) \Rightarrow c0])) (CHead e0 
-(Flat f0) u0) (CHead e (Flat f) u) H3) in ((let H5 \def (f_equal C F (\lambda 
-(e1: C).(match e1 in C return (\lambda (_: C).F) with [(CSort _) \Rightarrow 
-f0 | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).F) with 
-[(Bind _) \Rightarrow f0 | (Flat f1) \Rightarrow f1])])) (CHead e0 (Flat f0) 
-u0) (CHead e (Flat f) u) H3) in ((let H6 \def (f_equal C T (\lambda (e1: 
-C).(match e1 in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u0 | 
-(CHead _ _ t) \Rightarrow t])) (CHead e0 (Flat f0) u0) (CHead e (Flat f) u) 
-H3) in (\lambda (_: (eq F f0 f)).(\lambda (H8: (eq C e0 e)).(let H9 \def 
-(eq_ind C e0 (\lambda (c0: C).((eq C c0 (CHead e (Flat f) u)) \to (clear e 
-c))) H2 e H8) in (let H10 \def (eq_ind C e0 (\lambda (c0: C).(clear c0 c)) H1 
-e H8) in H10))))) H5)) H4))))))))) y x H0))) H))))).
-(* COMMENTS
-Initial nodes: 453
-END *)
-
-theorem clear_gen_flat_r:
- \forall (f: F).(\forall (x: C).(\forall (e: C).(\forall (u: T).((clear x 
-(CHead e (Flat f) u)) \to (\forall (P: Prop).P)))))
-\def
- \lambda (f: F).(\lambda (x: C).(\lambda (e: C).(\lambda (u: T).(\lambda (H: 
-(clear x (CHead e (Flat f) u))).(\lambda (P: Prop).(insert_eq C (CHead e 
-(Flat f) u) (\lambda (c: C).(clear x c)) (\lambda (_: C).P) (\lambda (y: 
-C).(\lambda (H0: (clear x y)).(clear_ind (\lambda (_: C).(\lambda (c0: 
-C).((eq C c0 (CHead e (Flat f) u)) \to P))) (\lambda (b: B).(\lambda (e0: 
-C).(\lambda (u0: T).(\lambda (H1: (eq C (CHead e0 (Bind b) u0) (CHead e (Flat 
-f) u))).(let H2 \def (eq_ind C (CHead e0 (Bind b) u0) (\lambda (ee: C).(match 
-ee in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | 
-(CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with 
-[(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])])) I (CHead e (Flat 
-f) u) H1) in (False_ind P H2)))))) (\lambda (e0: C).(\lambda (c: C).(\lambda 
-(H1: (clear e0 c)).(\lambda (H2: (((eq C c (CHead e (Flat f) u)) \to 
-P))).(\lambda (_: F).(\lambda (_: T).(\lambda (H3: (eq C c (CHead e (Flat f) 
-u))).(let H4 \def (eq_ind C c (\lambda (c0: C).((eq C c0 (CHead e (Flat f) 
-u)) \to P)) H2 (CHead e (Flat f) u) H3) in (let H5 \def (eq_ind C c (\lambda 
-(c0: C).(clear e0 c0)) H1 (CHead e (Flat f) u) H3) in (H4 (refl_equal C 
-(CHead e (Flat f) u)))))))))))) x y H0))) H)))))).
-(* COMMENTS
-Initial nodes: 303
-END *)
-
-theorem clear_gen_all:
- \forall (c1: C).(\forall (c2: C).((clear c1 c2) \to (ex_3 B C T (\lambda (b: 
-B).(\lambda (e: C).(\lambda (u: T).(eq C c2 (CHead e (Bind b) u))))))))
-\def
- \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (clear c1 c2)).(clear_ind 
-(\lambda (_: C).(\lambda (c0: C).(ex_3 B C T (\lambda (b: B).(\lambda (e: 
-C).(\lambda (u: T).(eq C c0 (CHead e (Bind b) u)))))))) (\lambda (b: 
-B).(\lambda (e: C).(\lambda (u: T).(ex_3_intro B C T (\lambda (b0: 
-B).(\lambda (e0: C).(\lambda (u0: T).(eq C (CHead e (Bind b) u) (CHead e0 
-(Bind b0) u0))))) b e u (refl_equal C (CHead e (Bind b) u)))))) (\lambda (e: 
-C).(\lambda (c: C).(\lambda (H0: (clear e c)).(\lambda (H1: (ex_3 B C T 
-(\lambda (b: B).(\lambda (e0: C).(\lambda (u: T).(eq C c (CHead e0 (Bind b) 
-u))))))).(\lambda (_: F).(\lambda (_: T).(let H2 \def H1 in (ex_3_ind B C T 
-(\lambda (b: B).(\lambda (e0: C).(\lambda (u0: T).(eq C c (CHead e0 (Bind b) 
-u0))))) (ex_3 B C T (\lambda (b: B).(\lambda (e0: C).(\lambda (u0: T).(eq C c 
-(CHead e0 (Bind b) u0)))))) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: 
-T).(\lambda (H3: (eq C c (CHead x1 (Bind x0) x2))).(let H4 \def (eq_ind C c 
-(\lambda (c0: C).(clear e c0)) H0 (CHead x1 (Bind x0) x2) H3) in (eq_ind_r C 
-(CHead x1 (Bind x0) x2) (\lambda (c0: C).(ex_3 B C T (\lambda (b: B).(\lambda 
-(e0: C).(\lambda (u0: T).(eq C c0 (CHead e0 (Bind b) u0))))))) (ex_3_intro B 
-C T (\lambda (b: B).(\lambda (e0: C).(\lambda (u0: T).(eq C (CHead x1 (Bind 
-x0) x2) (CHead e0 (Bind b) u0))))) x0 x1 x2 (refl_equal C (CHead x1 (Bind x0) 
-x2))) c H3)))))) H2)))))))) c1 c2 H))).
-(* COMMENTS
-Initial nodes: 381
-END *)
-