+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||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/getl/fwd.ma".
-
-include "Basic-1/drop/props.ma".
-
-include "Basic-1/clear/props.ma".
-
-theorem getl_refl:
- \forall (b: B).(\forall (c: C).(\forall (u: T).(getl O (CHead c (Bind b) u)
-(CHead c (Bind b) u))))
-\def
- \lambda (b: B).(\lambda (c: C).(\lambda (u: T).(getl_intro O (CHead c (Bind
-b) u) (CHead c (Bind b) u) (CHead c (Bind b) u) (drop_refl (CHead c (Bind b)
-u)) (clear_bind b c u)))).
-(* COMMENTS
-Initial nodes: 59
-END *)
-
-theorem getl_head:
- \forall (k: K).(\forall (h: nat).(\forall (c: C).(\forall (e: C).((getl (r k
-h) c e) \to (\forall (u: T).(getl (S h) (CHead c k u) e))))))
-\def
- \lambda (k: K).(\lambda (h: nat).(\lambda (c: C).(\lambda (e: C).(\lambda
-(H: (getl (r k h) c e)).(\lambda (u: T).(let H0 \def (getl_gen_all c e (r k
-h) H) in (ex2_ind C (\lambda (e0: C).(drop (r k h) O c e0)) (\lambda (e0:
-C).(clear e0 e)) (getl (S h) (CHead c k u) e) (\lambda (x: C).(\lambda (H1:
-(drop (r k h) O c x)).(\lambda (H2: (clear x e)).(getl_intro (S h) (CHead c k
-u) e x (drop_drop k h c x H1 u) H2)))) H0))))))).
-(* COMMENTS
-Initial nodes: 137
-END *)
-
-theorem getl_flat:
- \forall (c: C).(\forall (e: C).(\forall (h: nat).((getl h c e) \to (\forall
-(f: F).(\forall (u: T).(getl h (CHead c (Flat f) u) e))))))
-\def
- \lambda (c: C).(\lambda (e: C).(\lambda (h: nat).(\lambda (H: (getl h c
-e)).(\lambda (f: F).(\lambda (u: T).(let H0 \def (getl_gen_all c e h H) in
-(ex2_ind C (\lambda (e0: C).(drop h O c e0)) (\lambda (e0: C).(clear e0 e))
-(getl h (CHead c (Flat f) u) e) (\lambda (x: C).(\lambda (H1: (drop h O c
-x)).(\lambda (H2: (clear x e)).(nat_ind (\lambda (n: nat).((drop n O c x) \to
-(getl n (CHead c (Flat f) u) e))) (\lambda (H3: (drop O O c x)).(let H4 \def
-(eq_ind_r C x (\lambda (c0: C).(clear c0 e)) H2 c (drop_gen_refl c x H3)) in
-(getl_intro O (CHead c (Flat f) u) e (CHead c (Flat f) u) (drop_refl (CHead c
-(Flat f) u)) (clear_flat c e H4 f u)))) (\lambda (h0: nat).(\lambda (_:
-(((drop h0 O c x) \to (getl h0 (CHead c (Flat f) u) e)))).(\lambda (H3: (drop
-(S h0) O c x)).(getl_intro (S h0) (CHead c (Flat f) u) e x (drop_drop (Flat
-f) h0 c x H3 u) H2)))) h H1)))) H0))))))).
-(* COMMENTS
-Initial nodes: 285
-END *)
-
-theorem getl_ctail:
- \forall (b: B).(\forall (c: C).(\forall (d: C).(\forall (u: T).(\forall (i:
-nat).((getl i c (CHead d (Bind b) u)) \to (\forall (k: K).(\forall (v:
-T).(getl i (CTail k v c) (CHead (CTail k v d) (Bind b) u)))))))))
-\def
- \lambda (b: B).(\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i:
-nat).(\lambda (H: (getl i c (CHead d (Bind b) u))).(\lambda (k: K).(\lambda
-(v: T).(let H0 \def (getl_gen_all c (CHead d (Bind b) u) i H) in (ex2_ind C
-(\lambda (e: C).(drop i O c e)) (\lambda (e: C).(clear e (CHead d (Bind b)
-u))) (getl i (CTail k v c) (CHead (CTail k v d) (Bind b) u)) (\lambda (x:
-C).(\lambda (H1: (drop i O c x)).(\lambda (H2: (clear x (CHead d (Bind b)
-u))).(getl_intro i (CTail k v c) (CHead (CTail k v d) (Bind b) u) (CTail k v
-x) (drop_ctail c x O i H1 k v) (clear_ctail b x d u H2 k v))))) H0))))))))).
-(* COMMENTS
-Initial nodes: 203
-END *)
-
-theorem getl_mono:
- \forall (c: C).(\forall (x1: C).(\forall (h: nat).((getl h c x1) \to
-(\forall (x2: C).((getl h c x2) \to (eq C x1 x2))))))
-\def
- \lambda (c: C).(\lambda (x1: C).(\lambda (h: nat).(\lambda (H: (getl h c
-x1)).(\lambda (x2: C).(\lambda (H0: (getl h c x2)).(let H1 \def (getl_gen_all
-c x2 h H0) in (ex2_ind C (\lambda (e: C).(drop h O c e)) (\lambda (e:
-C).(clear e x2)) (eq C x1 x2) (\lambda (x: C).(\lambda (H2: (drop h O c
-x)).(\lambda (H3: (clear x x2)).(let H4 \def (getl_gen_all c x1 h H) in
-(ex2_ind C (\lambda (e: C).(drop h O c e)) (\lambda (e: C).(clear e x1)) (eq
-C x1 x2) (\lambda (x0: C).(\lambda (H5: (drop h O c x0)).(\lambda (H6: (clear
-x0 x1)).(let H7 \def (eq_ind C x (\lambda (c0: C).(drop h O c c0)) H2 x0
-(drop_mono c x O h H2 x0 H5)) in (let H8 \def (eq_ind_r C x0 (\lambda (c0:
-C).(drop h O c c0)) H7 x (drop_mono c x O h H2 x0 H5)) in (let H9 \def
-(eq_ind_r C x0 (\lambda (c0: C).(clear c0 x1)) H6 x (drop_mono c x O h H2 x0
-H5)) in (clear_mono x x1 H9 x2 H3))))))) H4))))) H1))))))).
-(* COMMENTS
-Initial nodes: 269
-END *)
-
projects / helm.git / blobdiff