+++ /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/clear/fwd.ma".
-
-theorem clear_clear:
- \forall (c1: C).(\forall (c2: C).((clear c1 c2) \to (clear c2 c2)))
-\def
- \lambda (c1: C).(C_ind (\lambda (c: C).(\forall (c2: C).((clear c c2) \to
-(clear c2 c2)))) (\lambda (n: nat).(\lambda (c2: C).(\lambda (H: (clear
-(CSort n) c2)).(clear_gen_sort c2 n H (clear c2 c2))))) (\lambda (c:
-C).(\lambda (H: ((\forall (c2: C).((clear c c2) \to (clear c2
-c2))))).(\lambda (k: K).(\lambda (t: T).(\lambda (c2: C).(\lambda (H0: (clear
-(CHead c k t) c2)).(K_ind (\lambda (k0: K).((clear (CHead c k0 t) c2) \to
-(clear c2 c2))) (\lambda (b: B).(\lambda (H1: (clear (CHead c (Bind b) t)
-c2)).(eq_ind_r C (CHead c (Bind b) t) (\lambda (c0: C).(clear c0 c0))
-(clear_bind b c t) c2 (clear_gen_bind b c c2 t H1)))) (\lambda (f:
-F).(\lambda (H1: (clear (CHead c (Flat f) t) c2)).(H c2 (clear_gen_flat f c
-c2 t H1)))) k H0))))))) c1).
-(* COMMENTS
-Initial nodes: 199
-END *)
-
-theorem clear_mono:
- \forall (c: C).(\forall (c1: C).((clear c c1) \to (\forall (c2: C).((clear c
-c2) \to (eq C c1 c2)))))
-\def
- \lambda (c: C).(C_ind (\lambda (c0: C).(\forall (c1: C).((clear c0 c1) \to
-(\forall (c2: C).((clear c0 c2) \to (eq C c1 c2)))))) (\lambda (n:
-nat).(\lambda (c1: C).(\lambda (_: (clear (CSort n) c1)).(\lambda (c2:
-C).(\lambda (H0: (clear (CSort n) c2)).(clear_gen_sort c2 n H0 (eq C c1
-c2))))))) (\lambda (c0: C).(\lambda (H: ((\forall (c1: C).((clear c0 c1) \to
-(\forall (c2: C).((clear c0 c2) \to (eq C c1 c2))))))).(\lambda (k:
-K).(\lambda (t: T).(\lambda (c1: C).(\lambda (H0: (clear (CHead c0 k t)
-c1)).(\lambda (c2: C).(\lambda (H1: (clear (CHead c0 k t) c2)).(K_ind
-(\lambda (k0: K).((clear (CHead c0 k0 t) c1) \to ((clear (CHead c0 k0 t) c2)
-\to (eq C c1 c2)))) (\lambda (b: B).(\lambda (H2: (clear (CHead c0 (Bind b)
-t) c1)).(\lambda (H3: (clear (CHead c0 (Bind b) t) c2)).(eq_ind_r C (CHead c0
-(Bind b) t) (\lambda (c3: C).(eq C c1 c3)) (eq_ind_r C (CHead c0 (Bind b) t)
-(\lambda (c3: C).(eq C c3 (CHead c0 (Bind b) t))) (refl_equal C (CHead c0
-(Bind b) t)) c1 (clear_gen_bind b c0 c1 t H2)) c2 (clear_gen_bind b c0 c2 t
-H3))))) (\lambda (f: F).(\lambda (H2: (clear (CHead c0 (Flat f) t)
-c1)).(\lambda (H3: (clear (CHead c0 (Flat f) t) c2)).(H c1 (clear_gen_flat f
-c0 c1 t H2) c2 (clear_gen_flat f c0 c2 t H3))))) k H0 H1))))))))) c).
-(* COMMENTS
-Initial nodes: 357
-END *)
-
-theorem clear_trans:
- \forall (c1: C).(\forall (c: C).((clear c1 c) \to (\forall (c2: C).((clear c
-c2) \to (clear c1 c2)))))
-\def
- \lambda (c1: C).(C_ind (\lambda (c: C).(\forall (c0: C).((clear c c0) \to
-(\forall (c2: C).((clear c0 c2) \to (clear c c2)))))) (\lambda (n:
-nat).(\lambda (c: C).(\lambda (H: (clear (CSort n) c)).(\lambda (c2:
-C).(\lambda (_: (clear c c2)).(clear_gen_sort c n H (clear (CSort n)
-c2))))))) (\lambda (c: C).(\lambda (H: ((\forall (c0: C).((clear c c0) \to
-(\forall (c2: C).((clear c0 c2) \to (clear c c2))))))).(\lambda (k:
-K).(\lambda (t: T).(\lambda (c0: C).(\lambda (H0: (clear (CHead c k t)
-c0)).(\lambda (c2: C).(\lambda (H1: (clear c0 c2)).(K_ind (\lambda (k0:
-K).((clear (CHead c k0 t) c0) \to (clear (CHead c k0 t) c2))) (\lambda (b:
-B).(\lambda (H2: (clear (CHead c (Bind b) t) c0)).(let H3 \def (eq_ind C c0
-(\lambda (c3: C).(clear c3 c2)) H1 (CHead c (Bind b) t) (clear_gen_bind b c
-c0 t H2)) in (eq_ind_r C (CHead c (Bind b) t) (\lambda (c3: C).(clear (CHead
-c (Bind b) t) c3)) (clear_bind b c t) c2 (clear_gen_bind b c c2 t H3)))))
-(\lambda (f: F).(\lambda (H2: (clear (CHead c (Flat f) t) c0)).(clear_flat c
-c2 (H c0 (clear_gen_flat f c c0 t H2) c2 H1) f t))) k H0))))))))) c1).
-(* COMMENTS
-Initial nodes: 299
-END *)
-
-theorem clear_ctail:
- \forall (b: B).(\forall (c1: C).(\forall (c2: C).(\forall (u2: T).((clear c1
-(CHead c2 (Bind b) u2)) \to (\forall (k: K).(\forall (u1: T).(clear (CTail k
-u1 c1) (CHead (CTail k u1 c2) (Bind b) u2))))))))
-\def
- \lambda (b: B).(\lambda (c1: C).(C_ind (\lambda (c: C).(\forall (c2:
-C).(\forall (u2: T).((clear c (CHead c2 (Bind b) u2)) \to (\forall (k:
-K).(\forall (u1: T).(clear (CTail k u1 c) (CHead (CTail k u1 c2) (Bind b)
-u2)))))))) (\lambda (n: nat).(\lambda (c2: C).(\lambda (u2: T).(\lambda (H:
-(clear (CSort n) (CHead c2 (Bind b) u2))).(\lambda (k: K).(\lambda (u1:
-T).(K_ind (\lambda (k0: K).(clear (CHead (CSort n) k0 u1) (CHead (CTail k0 u1
-c2) (Bind b) u2))) (\lambda (b0: B).(clear_gen_sort (CHead c2 (Bind b) u2) n
-H (clear (CHead (CSort n) (Bind b0) u1) (CHead (CTail (Bind b0) u1 c2) (Bind
-b) u2)))) (\lambda (f: F).(clear_gen_sort (CHead c2 (Bind b) u2) n H (clear
-(CHead (CSort n) (Flat f) u1) (CHead (CTail (Flat f) u1 c2) (Bind b) u2))))
-k))))))) (\lambda (c: C).(\lambda (H: ((\forall (c2: C).(\forall (u2:
-T).((clear c (CHead c2 (Bind b) u2)) \to (\forall (k: K).(\forall (u1:
-T).(clear (CTail k u1 c) (CHead (CTail k u1 c2) (Bind b) u2))))))))).(\lambda
-(k: K).(\lambda (t: T).(\lambda (c2: C).(\lambda (u2: T).(\lambda (H0: (clear
-(CHead c k t) (CHead c2 (Bind b) u2))).(\lambda (k0: K).(\lambda (u1:
-T).(K_ind (\lambda (k1: K).((clear (CHead c k1 t) (CHead c2 (Bind b) u2)) \to
-(clear (CHead (CTail k0 u1 c) k1 t) (CHead (CTail k0 u1 c2) (Bind b) u2))))
-(\lambda (b0: B).(\lambda (H1: (clear (CHead c (Bind b0) t) (CHead c2 (Bind
-b) u2))).(let H2 \def (f_equal C C (\lambda (e: C).(match e in C return
-(\lambda (_: C).C) with [(CSort _) \Rightarrow c2 | (CHead c0 _ _)
-\Rightarrow c0])) (CHead c2 (Bind b) u2) (CHead c (Bind b0) t)
-(clear_gen_bind b0 c (CHead c2 (Bind b) u2) t H1)) in ((let H3 \def (f_equal
-C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with [(CSort _)
-\Rightarrow b | (CHead _ k1 _) \Rightarrow (match k1 in K return (\lambda (_:
-K).B) with [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow b])])) (CHead c2
-(Bind b) u2) (CHead c (Bind b0) t) (clear_gen_bind b0 c (CHead c2 (Bind b)
-u2) t H1)) in ((let H4 \def (f_equal C T (\lambda (e: C).(match e in C return
-(\lambda (_: C).T) with [(CSort _) \Rightarrow u2 | (CHead _ _ t0)
-\Rightarrow t0])) (CHead c2 (Bind b) u2) (CHead c (Bind b0) t)
-(clear_gen_bind b0 c (CHead c2 (Bind b) u2) t H1)) in (\lambda (H5: (eq B b
-b0)).(\lambda (H6: (eq C c2 c)).(eq_ind_r T t (\lambda (t0: T).(clear (CHead
-(CTail k0 u1 c) (Bind b0) t) (CHead (CTail k0 u1 c2) (Bind b) t0))) (eq_ind_r
-C c (\lambda (c0: C).(clear (CHead (CTail k0 u1 c) (Bind b0) t) (CHead (CTail
-k0 u1 c0) (Bind b) t))) (eq_ind B b (\lambda (b1: B).(clear (CHead (CTail k0
-u1 c) (Bind b1) t) (CHead (CTail k0 u1 c) (Bind b) t))) (clear_bind b (CTail
-k0 u1 c) t) b0 H5) c2 H6) u2 H4)))) H3)) H2)))) (\lambda (f: F).(\lambda (H1:
-(clear (CHead c (Flat f) t) (CHead c2 (Bind b) u2))).(clear_flat (CTail k0 u1
-c) (CHead (CTail k0 u1 c2) (Bind b) u2) (H c2 u2 (clear_gen_flat f c (CHead
-c2 (Bind b) u2) t H1) k0 u1) f t))) k H0)))))))))) c1)).
-(* COMMENTS
-Initial nodes: 819
-END *)
-
-theorem clear_cle:
- \forall (c1: C).(\forall (c2: C).((clear c1 c2) \to (cle c2 c1)))
-\def
- \lambda (c1: C).(C_ind (\lambda (c: C).(\forall (c2: C).((clear c c2) \to
-(le (cweight c2) (cweight c))))) (\lambda (n: nat).(\lambda (c2: C).(\lambda
-(H: (clear (CSort n) c2)).(clear_gen_sort c2 n H (le (cweight c2) O)))))
-(\lambda (c: C).(\lambda (H: ((\forall (c2: C).((clear c c2) \to (le (cweight
-c2) (cweight c)))))).(\lambda (k: K).(\lambda (t: T).(\lambda (c2:
-C).(\lambda (H0: (clear (CHead c k t) c2)).(K_ind (\lambda (k0: K).((clear
-(CHead c k0 t) c2) \to (le (cweight c2) (plus (cweight c) (tweight t)))))
-(\lambda (b: B).(\lambda (H1: (clear (CHead c (Bind b) t) c2)).(eq_ind_r C
-(CHead c (Bind b) t) (\lambda (c0: C).(le (cweight c0) (plus (cweight c)
-(tweight t)))) (le_n (plus (cweight c) (tweight t))) c2 (clear_gen_bind b c
-c2 t H1)))) (\lambda (f: F).(\lambda (H1: (clear (CHead c (Flat f) t)
-c2)).(le_plus_trans (cweight c2) (cweight c) (tweight t) (H c2
-(clear_gen_flat f c c2 t H1))))) k H0))))))) c1).
-(* COMMENTS
-Initial nodes: 247
-END *)
-
projects / helm.git / blobdiff