X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1A%2Fcsubc%2Fclear.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1A%2Fcsubc%2Fclear.ma;h=5650cc9e77ed11a273ea4e41401b2fcdbd613d8d;hb=d2545ffd201b1aa49887313791386add78fa8603;hp=0000000000000000000000000000000000000000;hpb=57ae1762497a5f3ea75740e2908e04adb8642cc2;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_1A/csubc/clear.ma b/matita/matita/contribs/lambdadelta/basic_1A/csubc/clear.ma
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@@ -0,0 +1,167 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_1A/csubc/fwd.ma".
+
+include "basic_1A/clear/fwd.ma".
+
+lemma csubc_clear_conf:
+ \forall (g: G).(\forall (c1: C).(\forall (e1: C).((clear c1 e1) \to (\forall 
+(c2: C).((csubc g c1 c2) \to (ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda 
+(e2: C).(csubc g e1 e2))))))))
+\def
+ \lambda (g: G).(\lambda (c1: C).(\lambda (e1: C).(\lambda (H: (clear c1 
+e1)).(clear_ind (\lambda (c: C).(\lambda (c0: C).(\forall (c2: C).((csubc g c 
+c2) \to (ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda (e2: C).(csubc g c0 
+e2))))))) (\lambda (b: B).(\lambda (e: C).(\lambda (u: T).(\lambda (c2: 
+C).(\lambda (H0: (csubc g (CHead e (Bind b) u) c2)).(let H_x \def 
+(csubc_gen_head_l g e c2 u (Bind b) H0) in (let H1 \def H_x in (or3_ind (ex2 
+C (\lambda (c3: C).(eq C c2 (CHead c3 (Bind b) u))) (\lambda (c3: C).(csubc g 
+e c3))) (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq K 
+(Bind b) (Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (_: A).(eq 
+C c2 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_: T).(\lambda 
+(_: A).(csubc g e c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(sc3 
+g (asucc g a) e u)))) (\lambda (c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g 
+a c3 w))))) (ex4_3 B C T (\lambda (b0: B).(\lambda (c3: C).(\lambda (v2: 
+T).(eq C c2 (CHead c3 (Bind b0) v2))))) (\lambda (_: B).(\lambda (_: 
+C).(\lambda (_: T).(eq K (Bind b) (Bind Void))))) (\lambda (b0: B).(\lambda 
+(_: C).(\lambda (_: T).(not (eq B b0 Void))))) (\lambda (_: B).(\lambda (c3: 
+C).(\lambda (_: T).(csubc g e c3))))) (ex2 C (\lambda (e2: C).(clear c2 e2)) 
+(\lambda (e2: C).(csubc g (CHead e (Bind b) u) e2))) (\lambda (H2: (ex2 C 
+(\lambda (c3: C).(eq C c2 (CHead c3 (Bind b) u))) (\lambda (c3: C).(csubc g e 
+c3)))).(ex2_ind C (\lambda (c3: C).(eq C c2 (CHead c3 (Bind b) u))) (\lambda 
+(c3: C).(csubc g e c3)) (ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda (e2: 
+C).(csubc g (CHead e (Bind b) u) e2))) (\lambda (x: C).(\lambda (H3: (eq C c2 
+(CHead x (Bind b) u))).(\lambda (H4: (csubc g e x)).(eq_ind_r C (CHead x 
+(Bind b) u) (\lambda (c: C).(ex2 C (\lambda (e2: C).(clear c e2)) (\lambda 
+(e2: C).(csubc g (CHead e (Bind b) u) e2)))) (ex_intro2 C (\lambda (e2: 
+C).(clear (CHead x (Bind b) u) e2)) (\lambda (e2: C).(csubc g (CHead e (Bind 
+b) u) e2)) (CHead x (Bind b) u) (clear_bind b x u) (csubc_head g e x H4 (Bind 
+b) u)) c2 H3)))) H2)) (\lambda (H2: (ex5_3 C T A (\lambda (_: C).(\lambda (_: 
+T).(\lambda (_: A).(eq K (Bind b) (Bind Abst))))) (\lambda (c3: C).(\lambda 
+(w: T).(\lambda (_: A).(eq C c2 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: 
+C).(\lambda (_: T).(\lambda (_: A).(csubc g e c3)))) (\lambda (_: C).(\lambda 
+(_: T).(\lambda (a: A).(sc3 g (asucc g a) e u)))) (\lambda (c3: C).(\lambda 
+(w: T).(\lambda (a: A).(sc3 g a c3 w)))))).(ex5_3_ind C T A (\lambda (_: 
+C).(\lambda (_: T).(\lambda (_: A).(eq K (Bind b) (Bind Abst))))) (\lambda 
+(c3: C).(\lambda (w: T).(\lambda (_: A).(eq C c2 (CHead c3 (Bind Abbr) w))))) 
+(\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g e c3)))) (\lambda 
+(_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g (asucc g a) e u)))) (\lambda 
+(c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g a c3 w)))) (ex2 C (\lambda 
+(e2: C).(clear c2 e2)) (\lambda (e2: C).(csubc g (CHead e (Bind b) u) e2))) 
+(\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H3: (eq K (Bind 
+b) (Bind Abst))).(\lambda (H4: (eq C c2 (CHead x0 (Bind Abbr) x1))).(\lambda 
+(H5: (csubc g e x0)).(\lambda (H6: (sc3 g (asucc g x2) e u)).(\lambda (H7: 
+(sc3 g x2 x0 x1)).(eq_ind_r C (CHead x0 (Bind Abbr) x1) (\lambda (c: C).(ex2 
+C (\lambda (e2: C).(clear c e2)) (\lambda (e2: C).(csubc g (CHead e (Bind b) 
+u) e2)))) (let H8 \def (f_equal K B (\lambda (e0: K).(match e0 with [(Bind 
+b0) \Rightarrow b0 | (Flat _) \Rightarrow b])) (Bind b) (Bind Abst) H3) in 
+(eq_ind_r B Abst (\lambda (b0: B).(ex2 C (\lambda (e2: C).(clear (CHead x0 
+(Bind Abbr) x1) e2)) (\lambda (e2: C).(csubc g (CHead e (Bind b0) u) e2)))) 
+(ex_intro2 C (\lambda (e2: C).(clear (CHead x0 (Bind Abbr) x1) e2)) (\lambda 
+(e2: C).(csubc g (CHead e (Bind Abst) u) e2)) (CHead x0 (Bind Abbr) x1) 
+(clear_bind Abbr x0 x1) (csubc_abst g e x0 H5 u x2 H6 x1 H7)) b H8)) c2 
+H4))))))))) H2)) (\lambda (H2: (ex4_3 B C T (\lambda (b0: B).(\lambda (c3: 
+C).(\lambda (v2: T).(eq C c2 (CHead c3 (Bind b0) v2))))) (\lambda (_: 
+B).(\lambda (_: C).(\lambda (_: T).(eq K (Bind b) (Bind Void))))) (\lambda 
+(b0: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b0 Void))))) (\lambda (_: 
+B).(\lambda (c3: C).(\lambda (_: T).(csubc g e c3)))))).(ex4_3_ind B C T 
+(\lambda (b0: B).(\lambda (c3: C).(\lambda (v2: T).(eq C c2 (CHead c3 (Bind 
+b0) v2))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(eq K (Bind b) 
+(Bind Void))))) (\lambda (b0: B).(\lambda (_: C).(\lambda (_: T).(not (eq B 
+b0 Void))))) (\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc g e 
+c3)))) (ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda (e2: C).(csubc g 
+(CHead e (Bind b) u) e2))) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: 
+T).(\lambda (H3: (eq C c2 (CHead x1 (Bind x0) x2))).(\lambda (H4: (eq K (Bind 
+b) (Bind Void))).(\lambda (H5: (not (eq B x0 Void))).(\lambda (H6: (csubc g e 
+x1)).(eq_ind_r C (CHead x1 (Bind x0) x2) (\lambda (c: C).(ex2 C (\lambda (e2: 
+C).(clear c e2)) (\lambda (e2: C).(csubc g (CHead e (Bind b) u) e2)))) (let 
+H7 \def (f_equal K B (\lambda (e0: K).(match e0 with [(Bind b0) \Rightarrow 
+b0 | (Flat _) \Rightarrow b])) (Bind b) (Bind Void) H4) in (eq_ind_r B Void 
+(\lambda (b0: B).(ex2 C (\lambda (e2: C).(clear (CHead x1 (Bind x0) x2) e2)) 
+(\lambda (e2: C).(csubc g (CHead e (Bind b0) u) e2)))) (ex_intro2 C (\lambda 
+(e2: C).(clear (CHead x1 (Bind x0) x2) e2)) (\lambda (e2: C).(csubc g (CHead 
+e (Bind Void) u) e2)) (CHead x1 (Bind x0) x2) (clear_bind x0 x1 x2) 
+(csubc_void g e x1 H6 x0 H5 u x2)) b H7)) c2 H3)))))))) H2)) H1)))))))) 
+(\lambda (e: C).(\lambda (c: C).(\lambda (_: (clear e c)).(\lambda (H1: 
+((\forall (c2: C).((csubc g e c2) \to (ex2 C (\lambda (e2: C).(clear c2 e2)) 
+(\lambda (e2: C).(csubc g c e2))))))).(\lambda (f: F).(\lambda (u: 
+T).(\lambda (c2: C).(\lambda (H2: (csubc g (CHead e (Flat f) u) c2)).(let H_x 
+\def (csubc_gen_head_l g e c2 u (Flat f) H2) in (let H3 \def H_x in (or3_ind 
+(ex2 C (\lambda (c3: C).(eq C c2 (CHead c3 (Flat f) u))) (\lambda (c3: 
+C).(csubc g e c3))) (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: 
+A).(eq K (Flat f) (Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda 
+(_: A).(eq C c2 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_: 
+T).(\lambda (_: A).(csubc g e c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda 
+(a: A).(sc3 g (asucc g a) e u)))) (\lambda (c3: C).(\lambda (w: T).(\lambda 
+(a: A).(sc3 g a c3 w))))) (ex4_3 B C T (\lambda (b: B).(\lambda (c3: 
+C).(\lambda (v2: T).(eq C c2 (CHead c3 (Bind b) v2))))) (\lambda (_: 
+B).(\lambda (_: C).(\lambda (_: T).(eq K (Flat f) (Bind Void))))) (\lambda 
+(b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_: 
+B).(\lambda (c3: C).(\lambda (_: T).(csubc g e c3))))) (ex2 C (\lambda (e2: 
+C).(clear c2 e2)) (\lambda (e2: C).(csubc g c e2))) (\lambda (H4: (ex2 C 
+(\lambda (c3: C).(eq C c2 (CHead c3 (Flat f) u))) (\lambda (c3: C).(csubc g e 
+c3)))).(ex2_ind C (\lambda (c3: C).(eq C c2 (CHead c3 (Flat f) u))) (\lambda 
+(c3: C).(csubc g e c3)) (ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda (e2: 
+C).(csubc g c e2))) (\lambda (x: C).(\lambda (H5: (eq C c2 (CHead x (Flat f) 
+u))).(\lambda (H6: (csubc g e x)).(eq_ind_r C (CHead x (Flat f) u) (\lambda 
+(c0: C).(ex2 C (\lambda (e2: C).(clear c0 e2)) (\lambda (e2: C).(csubc g c 
+e2)))) (let H_x0 \def (H1 x H6) in (let H7 \def H_x0 in (ex2_ind C (\lambda 
+(e2: C).(clear x e2)) (\lambda (e2: C).(csubc g c e2)) (ex2 C (\lambda (e2: 
+C).(clear (CHead x (Flat f) u) e2)) (\lambda (e2: C).(csubc g c e2))) 
+(\lambda (x0: C).(\lambda (H8: (clear x x0)).(\lambda (H9: (csubc g c 
+x0)).(ex_intro2 C (\lambda (e2: C).(clear (CHead x (Flat f) u) e2)) (\lambda 
+(e2: C).(csubc g c e2)) x0 (clear_flat x x0 H8 f u) H9)))) H7))) c2 H5)))) 
+H4)) (\lambda (H4: (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: 
+A).(eq K (Flat f) (Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda 
+(_: A).(eq C c2 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_: 
+T).(\lambda (_: A).(csubc g e c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda 
+(a: A).(sc3 g (asucc g a) e u)))) (\lambda (c3: C).(\lambda (w: T).(\lambda 
+(a: A).(sc3 g a c3 w)))))).(ex5_3_ind C T A (\lambda (_: C).(\lambda (_: 
+T).(\lambda (_: A).(eq K (Flat f) (Bind Abst))))) (\lambda (c3: C).(\lambda 
+(w: T).(\lambda (_: A).(eq C c2 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: 
+C).(\lambda (_: T).(\lambda (_: A).(csubc g e c3)))) (\lambda (_: C).(\lambda 
+(_: T).(\lambda (a: A).(sc3 g (asucc g a) e u)))) (\lambda (c3: C).(\lambda 
+(w: T).(\lambda (a: A).(sc3 g a c3 w)))) (ex2 C (\lambda (e2: C).(clear c2 
+e2)) (\lambda (e2: C).(csubc g c e2))) (\lambda (x0: C).(\lambda (x1: 
+T).(\lambda (x2: A).(\lambda (H5: (eq K (Flat f) (Bind Abst))).(\lambda (H6: 
+(eq C c2 (CHead x0 (Bind Abbr) x1))).(\lambda (_: (csubc g e x0)).(\lambda 
+(_: (sc3 g (asucc g x2) e u)).(\lambda (_: (sc3 g x2 x0 x1)).(eq_ind_r C 
+(CHead x0 (Bind Abbr) x1) (\lambda (c0: C).(ex2 C (\lambda (e2: C).(clear c0 
+e2)) (\lambda (e2: C).(csubc g c e2)))) (let H10 \def (eq_ind K (Flat f) 
+(\lambda (ee: K).(match ee with [(Bind _) \Rightarrow False | (Flat _) 
+\Rightarrow True])) I (Bind Abst) H5) in (False_ind (ex2 C (\lambda (e2: 
+C).(clear (CHead x0 (Bind Abbr) x1) e2)) (\lambda (e2: C).(csubc g c e2))) 
+H10)) c2 H6))))))))) H4)) (\lambda (H4: (ex4_3 B C T (\lambda (b: B).(\lambda 
+(c3: C).(\lambda (v2: T).(eq C c2 (CHead c3 (Bind b) v2))))) (\lambda (_: 
+B).(\lambda (_: C).(\lambda (_: T).(eq K (Flat f) (Bind Void))))) (\lambda 
+(b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_: 
+B).(\lambda (c3: C).(\lambda (_: T).(csubc g e c3)))))).(ex4_3_ind B C T 
+(\lambda (b: B).(\lambda (c3: C).(\lambda (v2: T).(eq C c2 (CHead c3 (Bind b) 
+v2))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(eq K (Flat f) (Bind 
+Void))))) (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b 
+Void))))) (\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc g e c3)))) 
+(ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda (e2: C).(csubc g c e2))) 
+(\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda (H5: (eq C c2 
+(CHead x1 (Bind x0) x2))).(\lambda (H6: (eq K (Flat f) (Bind Void))).(\lambda 
+(_: (not (eq B x0 Void))).(\lambda (_: (csubc g e x1)).(eq_ind_r C (CHead x1 
+(Bind x0) x2) (\lambda (c0: C).(ex2 C (\lambda (e2: C).(clear c0 e2)) 
+(\lambda (e2: C).(csubc g c e2)))) (let H9 \def (eq_ind K (Flat f) (\lambda 
+(ee: K).(match ee with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow 
+True])) I (Bind Void) H6) in (False_ind (ex2 C (\lambda (e2: C).(clear (CHead 
+x1 (Bind x0) x2) e2)) (\lambda (e2: C).(csubc g c e2))) H9)) c2 H5)))))))) 
+H4)) H3))))))))))) c1 e1 H)))).
+