X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fcontribs%2FLAMBDA-TYPES%2FLambdaDelta-1%2Fgetl%2Ffwd.ma;fp=matita%2Fcontribs%2FLAMBDA-TYPES%2FLambdaDelta-1%2Fgetl%2Ffwd.ma;h=af9a9fb9780dd063e1d657dd7e77fa7a1a1b7d3e;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/getl/fwd.ma b/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/getl/fwd.ma new file mode 100644 index 000000000..af9a9fb97 --- /dev/null +++ b/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/getl/fwd.ma @@ -0,0 +1,105 @@ +(**************************************************************************) +(* ___ *) +(* ||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 "LambdaDelta-1/getl/defs.ma". + +include "LambdaDelta-1/drop/fwd.ma". + +include "LambdaDelta-1/clear/fwd.ma". + +theorem getl_gen_all: + \forall (c1: C).(\forall (c2: C).(\forall (i: nat).((getl i c1 c2) \to (ex2 +C (\lambda (e: C).(drop i O c1 e)) (\lambda (e: C).(clear e c2)))))) +\def + \lambda (c1: C).(\lambda (c2: C).(\lambda (i: nat).(\lambda (H: (getl i c1 +c2)).(getl_ind i c1 c2 (ex2 C (\lambda (e: C).(drop i O c1 e)) (\lambda (e: +C).(clear e c2))) (\lambda (e: C).(\lambda (H0: (drop i O c1 e)).(\lambda +(H1: (clear e c2)).(ex_intro2 C (\lambda (e0: C).(drop i O c1 e0)) (\lambda +(e0: C).(clear e0 c2)) e H0 H1)))) H)))). + +theorem getl_gen_sort: + \forall (n: nat).(\forall (h: nat).(\forall (x: C).((getl h (CSort n) x) \to +(\forall (P: Prop).P)))) +\def + \lambda (n: nat).(\lambda (h: nat).(\lambda (x: C).(\lambda (H: (getl h +(CSort n) x)).(\lambda (P: Prop).(let H0 \def (getl_gen_all (CSort n) x h H) +in (ex2_ind C (\lambda (e: C).(drop h O (CSort n) e)) (\lambda (e: C).(clear +e x)) P (\lambda (x0: C).(\lambda (H1: (drop h O (CSort n) x0)).(\lambda (H2: +(clear x0 x)).(and3_ind (eq C x0 (CSort n)) (eq nat h O) (eq nat O O) P +(\lambda (H3: (eq C x0 (CSort n))).(\lambda (_: (eq nat h O)).(\lambda (_: +(eq nat O O)).(let H6 \def (eq_ind C x0 (\lambda (c: C).(clear c x)) H2 +(CSort n) H3) in (clear_gen_sort x n H6 P))))) (drop_gen_sort n h O x0 +H1))))) H0)))))). + +theorem getl_gen_O: + \forall (e: C).(\forall (x: C).((getl O e x) \to (clear e x))) +\def + \lambda (e: C).(\lambda (x: C).(\lambda (H: (getl O e x)).(let H0 \def +(getl_gen_all e x O H) in (ex2_ind C (\lambda (e0: C).(drop O O e e0)) +(\lambda (e0: C).(clear e0 x)) (clear e x) (\lambda (x0: C).(\lambda (H1: +(drop O O e x0)).(\lambda (H2: (clear x0 x)).(let H3 \def (eq_ind_r C x0 +(\lambda (c: C).(clear c x)) H2 e (drop_gen_refl e x0 H1)) in H3)))) H0)))). + +theorem getl_gen_S: + \forall (k: K).(\forall (c: C).(\forall (x: C).(\forall (u: T).(\forall (h: +nat).((getl (S h) (CHead c k u) x) \to (getl (r k h) c x)))))) +\def + \lambda (k: K).(\lambda (c: C).(\lambda (x: C).(\lambda (u: T).(\lambda (h: +nat).(\lambda (H: (getl (S h) (CHead c k u) x)).(let H0 \def (getl_gen_all +(CHead c k u) x (S h) H) in (ex2_ind C (\lambda (e: C).(drop (S h) O (CHead c +k u) e)) (\lambda (e: C).(clear e x)) (getl (r k h) c x) (\lambda (x0: +C).(\lambda (H1: (drop (S h) O (CHead c k u) x0)).(\lambda (H2: (clear x0 +x)).(getl_intro (r k h) c x x0 (drop_gen_drop k c x0 u h H1) H2)))) H0))))))). + +theorem getl_gen_flat: + \forall (f: F).(\forall (e: C).(\forall (d: C).(\forall (v: T).(\forall (i: +nat).((getl i (CHead e (Flat f) v) d) \to (getl i e d)))))) +\def + \lambda (f: F).(\lambda (e: C).(\lambda (d: C).(\lambda (v: T).(\lambda (i: +nat).(nat_ind (\lambda (n: nat).((getl n (CHead e (Flat f) v) d) \to (getl n +e d))) (\lambda (H: (getl O (CHead e (Flat f) v) d)).(getl_intro O e d e +(drop_refl e) (clear_gen_flat f e d v (getl_gen_O (CHead e (Flat f) v) d +H)))) (\lambda (n: nat).(\lambda (_: (((getl n (CHead e (Flat f) v) d) \to +(getl n e d)))).(\lambda (H0: (getl (S n) (CHead e (Flat f) v) +d)).(getl_gen_S (Flat f) e d v n H0)))) i))))). + +theorem getl_gen_bind: + \forall (b: B).(\forall (e: C).(\forall (d: C).(\forall (v: T).(\forall (i: +nat).((getl i (CHead e (Bind b) v) d) \to (or (land (eq nat i O) (eq C d +(CHead e (Bind b) v))) (ex2 nat (\lambda (j: nat).(eq nat i (S j))) (\lambda +(j: nat).(getl j e d))))))))) +\def + \lambda (b: B).(\lambda (e: C).(\lambda (d: C).(\lambda (v: T).(\lambda (i: +nat).(nat_ind (\lambda (n: nat).((getl n (CHead e (Bind b) v) d) \to (or +(land (eq nat n O) (eq C d (CHead e (Bind b) v))) (ex2 nat (\lambda (j: +nat).(eq nat n (S j))) (\lambda (j: nat).(getl j e d)))))) (\lambda (H: (getl +O (CHead e (Bind b) v) d)).(eq_ind_r C (CHead e (Bind b) v) (\lambda (c: +C).(or (land (eq nat O O) (eq C c (CHead e (Bind b) v))) (ex2 nat (\lambda +(j: nat).(eq nat O (S j))) (\lambda (j: nat).(getl j e c))))) (or_introl +(land (eq nat O O) (eq C (CHead e (Bind b) v) (CHead e (Bind b) v))) (ex2 nat +(\lambda (j: nat).(eq nat O (S j))) (\lambda (j: nat).(getl j e (CHead e +(Bind b) v)))) (conj (eq nat O O) (eq C (CHead e (Bind b) v) (CHead e (Bind +b) v)) (refl_equal nat O) (refl_equal C (CHead e (Bind b) v)))) d +(clear_gen_bind b e d v (getl_gen_O (CHead e (Bind b) v) d H)))) (\lambda (n: +nat).(\lambda (_: (((getl n (CHead e (Bind b) v) d) \to (or (land (eq nat n +O) (eq C d (CHead e (Bind b) v))) (ex2 nat (\lambda (j: nat).(eq nat n (S +j))) (\lambda (j: nat).(getl j e d))))))).(\lambda (H0: (getl (S n) (CHead e +(Bind b) v) d)).(or_intror (land (eq nat (S n) O) (eq C d (CHead e (Bind b) +v))) (ex2 nat (\lambda (j: nat).(eq nat (S n) (S j))) (\lambda (j: nat).(getl +j e d))) (ex_intro2 nat (\lambda (j: nat).(eq nat (S n) (S j))) (\lambda (j: +nat).(getl j e d)) n (refl_equal nat (S n)) (getl_gen_S (Bind b) e d v n +H0)))))) i))))). +