+++ /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/csubv/fwd.ma".
-
-include "basic_1/clear/fwd.ma".
-
-lemma csubv_clear_conf:
- \forall (c1: C).(\forall (c2: C).((csubv c1 c2) \to (\forall (b1:
-B).(\forall (d1: C).(\forall (v1: T).((clear c1 (CHead d1 (Bind b1) v1)) \to
-(ex2_3 B C T (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csubv d1
-d2)))) (\lambda (b2: B).(\lambda (d2: C).(\lambda (v2: T).(clear c2 (CHead d2
-(Bind b2) v2))))))))))))
-\def
- \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (csubv c1 c2)).(csubv_ind
-(\lambda (c: C).(\lambda (c0: C).(\forall (b1: B).(\forall (d1: C).(\forall
-(v1: T).((clear c (CHead d1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (_:
-B).(\lambda (d2: C).(\lambda (_: T).(csubv d1 d2)))) (\lambda (b2:
-B).(\lambda (d2: C).(\lambda (v2: T).(clear c0 (CHead d2 (Bind b2)
-v2)))))))))))) (\lambda (n: nat).(\lambda (b1: B).(\lambda (d1: C).(\lambda
-(v1: T).(\lambda (H0: (clear (CSort n) (CHead d1 (Bind b1)
-v1))).(clear_gen_sort (CHead d1 (Bind b1) v1) n H0 (ex2_3 B C T (\lambda (_:
-B).(\lambda (d2: C).(\lambda (_: T).(csubv d1 d2)))) (\lambda (b2:
-B).(\lambda (d2: C).(\lambda (v2: T).(clear (CSort n) (CHead d2 (Bind b2)
-v2)))))))))))) (\lambda (c3: C).(\lambda (c4: C).(\lambda (H0: (csubv c3
-c4)).(\lambda (_: ((\forall (b1: B).(\forall (d1: C).(\forall (v1: T).((clear
-c3 (CHead d1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (_: B).(\lambda (d2:
-C).(\lambda (_: T).(csubv d1 d2)))) (\lambda (b2: B).(\lambda (d2:
-C).(\lambda (v2: T).(clear c4 (CHead d2 (Bind b2) v2)))))))))))).(\lambda
-(v1: T).(\lambda (v2: T).(\lambda (b1: B).(\lambda (d1: C).(\lambda (v0:
-T).(\lambda (H2: (clear (CHead c3 (Bind Void) v1) (CHead d1 (Bind b1)
-v0))).(let H3 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _)
-\Rightarrow d1 | (CHead c _ _) \Rightarrow c])) (CHead d1 (Bind b1) v0)
-(CHead c3 (Bind Void) v1) (clear_gen_bind Void c3 (CHead d1 (Bind b1) v0) v1
-H2)) in ((let H4 \def (f_equal C B (\lambda (e: C).(match e with [(CSort _)
-\Rightarrow b1 | (CHead _ k _) \Rightarrow (match k with [(Bind b)
-\Rightarrow b | (Flat _) \Rightarrow b1])])) (CHead d1 (Bind b1) v0) (CHead
-c3 (Bind Void) v1) (clear_gen_bind Void c3 (CHead d1 (Bind b1) v0) v1 H2)) in
-((let H5 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _)
-\Rightarrow v0 | (CHead _ _ t) \Rightarrow t])) (CHead d1 (Bind b1) v0)
-(CHead c3 (Bind Void) v1) (clear_gen_bind Void c3 (CHead d1 (Bind b1) v0) v1
-H2)) in (\lambda (_: (eq B b1 Void)).(\lambda (H7: (eq C d1 c3)).(eq_ind_r C
-c3 (\lambda (c: C).(ex2_3 B C T (\lambda (_: B).(\lambda (d2: C).(\lambda (_:
-T).(csubv c d2)))) (\lambda (b2: B).(\lambda (d2: C).(\lambda (v3: T).(clear
-(CHead c4 (Bind Void) v2) (CHead d2 (Bind b2) v3))))))) (ex2_3_intro B C T
-(\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csubv c3 d2)))) (\lambda
-(b2: B).(\lambda (d2: C).(\lambda (v3: T).(clear (CHead c4 (Bind Void) v2)
-(CHead d2 (Bind b2) v3))))) Void c4 v2 H0 (clear_bind Void c4 v2)) d1 H7))))
-H4)) H3)))))))))))) (\lambda (c3: C).(\lambda (c4: C).(\lambda (H0: (csubv c3
-c4)).(\lambda (_: ((\forall (b1: B).(\forall (d1: C).(\forall (v1: T).((clear
-c3 (CHead d1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (_: B).(\lambda (d2:
-C).(\lambda (_: T).(csubv d1 d2)))) (\lambda (b2: B).(\lambda (d2:
-C).(\lambda (v2: T).(clear c4 (CHead d2 (Bind b2) v2)))))))))))).(\lambda
-(b1: B).(\lambda (_: (not (eq B b1 Void))).(\lambda (b2: B).(\lambda (v1:
-T).(\lambda (v2: T).(\lambda (b0: B).(\lambda (d1: C).(\lambda (v0:
-T).(\lambda (H3: (clear (CHead c3 (Bind b1) v1) (CHead d1 (Bind b0)
-v0))).(let H4 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _)
-\Rightarrow d1 | (CHead c _ _) \Rightarrow c])) (CHead d1 (Bind b0) v0)
-(CHead c3 (Bind b1) v1) (clear_gen_bind b1 c3 (CHead d1 (Bind b0) v0) v1 H3))
-in ((let H5 \def (f_equal C B (\lambda (e: C).(match e with [(CSort _)
-\Rightarrow b0 | (CHead _ k _) \Rightarrow (match k with [(Bind b)
-\Rightarrow b | (Flat _) \Rightarrow b0])])) (CHead d1 (Bind b0) v0) (CHead
-c3 (Bind b1) v1) (clear_gen_bind b1 c3 (CHead d1 (Bind b0) v0) v1 H3)) in
-((let H6 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _)
-\Rightarrow v0 | (CHead _ _ t) \Rightarrow t])) (CHead d1 (Bind b0) v0)
-(CHead c3 (Bind b1) v1) (clear_gen_bind b1 c3 (CHead d1 (Bind b0) v0) v1 H3))
-in (\lambda (_: (eq B b0 b1)).(\lambda (H8: (eq C d1 c3)).(eq_ind_r C c3
-(\lambda (c: C).(ex2_3 B C T (\lambda (_: B).(\lambda (d2: C).(\lambda (_:
-T).(csubv c d2)))) (\lambda (b3: B).(\lambda (d2: C).(\lambda (v3: T).(clear
-(CHead c4 (Bind b2) v2) (CHead d2 (Bind b3) v3))))))) (ex2_3_intro B C T
-(\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csubv c3 d2)))) (\lambda
-(b3: B).(\lambda (d2: C).(\lambda (v3: T).(clear (CHead c4 (Bind b2) v2)
-(CHead d2 (Bind b3) v3))))) b2 c4 v2 H0 (clear_bind b2 c4 v2)) d1 H8)))) H5))
-H4))))))))))))))) (\lambda (c3: C).(\lambda (c4: C).(\lambda (_: (csubv c3
-c4)).(\lambda (H1: ((\forall (b1: B).(\forall (d1: C).(\forall (v1:
-T).((clear c3 (CHead d1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (_:
-B).(\lambda (d2: C).(\lambda (_: T).(csubv d1 d2)))) (\lambda (b2:
-B).(\lambda (d2: C).(\lambda (v2: T).(clear c4 (CHead d2 (Bind b2)
-v2)))))))))))).(\lambda (f1: F).(\lambda (f2: F).(\lambda (v1: T).(\lambda
-(v2: T).(\lambda (b1: B).(\lambda (d1: C).(\lambda (v0: T).(\lambda (H2:
-(clear (CHead c3 (Flat f1) v1) (CHead d1 (Bind b1) v0))).(let H_x \def (H1 b1
-d1 v0 (clear_gen_flat f1 c3 (CHead d1 (Bind b1) v0) v1 H2)) in (let H3 \def
-H_x in (ex2_3_ind B C T (\lambda (_: B).(\lambda (d2: C).(\lambda (_:
-T).(csubv d1 d2)))) (\lambda (b2: B).(\lambda (d2: C).(\lambda (v3: T).(clear
-c4 (CHead d2 (Bind b2) v3))))) (ex2_3 B C T (\lambda (_: B).(\lambda (d2:
-C).(\lambda (_: T).(csubv d1 d2)))) (\lambda (b2: B).(\lambda (d2:
-C).(\lambda (v3: T).(clear (CHead c4 (Flat f2) v2) (CHead d2 (Bind b2)
-v3)))))) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda (H4:
-(csubv d1 x1)).(\lambda (H5: (clear c4 (CHead x1 (Bind x0) x2))).(ex2_3_intro
-B C T (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csubv d1 d2))))
-(\lambda (b2: B).(\lambda (d2: C).(\lambda (v3: T).(clear (CHead c4 (Flat f2)
-v2) (CHead d2 (Bind b2) v3))))) x0 x1 x2 H4 (clear_flat c4 (CHead x1 (Bind
-x0) x2) H5 f2 v2))))))) H3))))))))))))))) c1 c2 H))).
-
-lemma csubv_clear_conf_void:
- \forall (c1: C).(\forall (c2: C).((csubv c1 c2) \to (\forall (d1:
-C).(\forall (v1: T).((clear c1 (CHead d1 (Bind Void) v1)) \to (ex2_2 C T
-(\lambda (d2: C).(\lambda (_: T).(csubv d1 d2))) (\lambda (d2: C).(\lambda
-(v2: T).(clear c2 (CHead d2 (Bind Void) v2))))))))))
-\def
- \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (csubv c1 c2)).(csubv_ind
-(\lambda (c: C).(\lambda (c0: C).(\forall (d1: C).(\forall (v1: T).((clear c
-(CHead d1 (Bind Void) v1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (_:
-T).(csubv d1 d2))) (\lambda (d2: C).(\lambda (v2: T).(clear c0 (CHead d2
-(Bind Void) v2)))))))))) (\lambda (n: nat).(\lambda (d1: C).(\lambda (v1:
-T).(\lambda (H0: (clear (CSort n) (CHead d1 (Bind Void) v1))).(clear_gen_sort
-(CHead d1 (Bind Void) v1) n H0 (ex2_2 C T (\lambda (d2: C).(\lambda (_:
-T).(csubv d1 d2))) (\lambda (d2: C).(\lambda (v2: T).(clear (CSort n) (CHead
-d2 (Bind Void) v2)))))))))) (\lambda (c3: C).(\lambda (c4: C).(\lambda (H0:
-(csubv c3 c4)).(\lambda (_: ((\forall (d1: C).(\forall (v1: T).((clear c3
-(CHead d1 (Bind Void) v1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (_:
-T).(csubv d1 d2))) (\lambda (d2: C).(\lambda (v2: T).(clear c4 (CHead d2
-(Bind Void) v2)))))))))).(\lambda (v1: T).(\lambda (v2: T).(\lambda (d1:
-C).(\lambda (v0: T).(\lambda (H2: (clear (CHead c3 (Bind Void) v1) (CHead d1
-(Bind Void) v0))).(let H3 \def (f_equal C C (\lambda (e: C).(match e with
-[(CSort _) \Rightarrow d1 | (CHead c _ _) \Rightarrow c])) (CHead d1 (Bind
-Void) v0) (CHead c3 (Bind Void) v1) (clear_gen_bind Void c3 (CHead d1 (Bind
-Void) v0) v1 H2)) in ((let H4 \def (f_equal C T (\lambda (e: C).(match e with
-[(CSort _) \Rightarrow v0 | (CHead _ _ t) \Rightarrow t])) (CHead d1 (Bind
-Void) v0) (CHead c3 (Bind Void) v1) (clear_gen_bind Void c3 (CHead d1 (Bind
-Void) v0) v1 H2)) in (\lambda (H5: (eq C d1 c3)).(eq_ind_r C c3 (\lambda (c:
-C).(ex2_2 C T (\lambda (d2: C).(\lambda (_: T).(csubv c d2))) (\lambda (d2:
-C).(\lambda (v3: T).(clear (CHead c4 (Bind Void) v2) (CHead d2 (Bind Void)
-v3)))))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (_: T).(csubv c3 d2)))
-(\lambda (d2: C).(\lambda (v3: T).(clear (CHead c4 (Bind Void) v2) (CHead d2
-(Bind Void) v3)))) c4 v2 H0 (clear_bind Void c4 v2)) d1 H5))) H3)))))))))))
-(\lambda (c3: C).(\lambda (c4: C).(\lambda (_: (csubv c3 c4)).(\lambda (_:
-((\forall (d1: C).(\forall (v1: T).((clear c3 (CHead d1 (Bind Void) v1)) \to
-(ex2_2 C T (\lambda (d2: C).(\lambda (_: T).(csubv d1 d2))) (\lambda (d2:
-C).(\lambda (v2: T).(clear c4 (CHead d2 (Bind Void) v2)))))))))).(\lambda
-(b1: B).(\lambda (H2: (not (eq B b1 Void))).(\lambda (b2: B).(\lambda (v1:
-T).(\lambda (v2: T).(\lambda (d1: C).(\lambda (v0: T).(\lambda (H3: (clear
-(CHead c3 (Bind b1) v1) (CHead d1 (Bind Void) v0))).(let H4 \def (f_equal C C
-(\lambda (e: C).(match e with [(CSort _) \Rightarrow d1 | (CHead c _ _)
-\Rightarrow c])) (CHead d1 (Bind Void) v0) (CHead c3 (Bind b1) v1)
-(clear_gen_bind b1 c3 (CHead d1 (Bind Void) v0) v1 H3)) in ((let H5 \def
-(f_equal C B (\lambda (e: C).(match e with [(CSort _) \Rightarrow Void |
-(CHead _ k _) \Rightarrow (match k with [(Bind b) \Rightarrow b | (Flat _)
-\Rightarrow Void])])) (CHead d1 (Bind Void) v0) (CHead c3 (Bind b1) v1)
-(clear_gen_bind b1 c3 (CHead d1 (Bind Void) v0) v1 H3)) in ((let H6 \def
-(f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow v0 | (CHead
-_ _ t) \Rightarrow t])) (CHead d1 (Bind Void) v0) (CHead c3 (Bind b1) v1)
-(clear_gen_bind b1 c3 (CHead d1 (Bind Void) v0) v1 H3)) in (\lambda (H7: (eq
-B Void b1)).(\lambda (H8: (eq C d1 c3)).(eq_ind_r C c3 (\lambda (c: C).(ex2_2
-C T (\lambda (d2: C).(\lambda (_: T).(csubv c d2))) (\lambda (d2: C).(\lambda
-(v3: T).(clear (CHead c4 (Bind b2) v2) (CHead d2 (Bind Void) v3)))))) (let H9
-\def (eq_ind_r B b1 (\lambda (b: B).(not (eq B b Void))) H2 Void H7) in (let
-H10 \def (match (H9 (refl_equal B Void)) in False with []) in H10)) d1 H8))))
-H5)) H4)))))))))))))) (\lambda (c3: C).(\lambda (c4: C).(\lambda (_: (csubv
-c3 c4)).(\lambda (H1: ((\forall (d1: C).(\forall (v1: T).((clear c3 (CHead d1
-(Bind Void) v1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (_: T).(csubv d1
-d2))) (\lambda (d2: C).(\lambda (v2: T).(clear c4 (CHead d2 (Bind Void)
-v2)))))))))).(\lambda (f1: F).(\lambda (f2: F).(\lambda (v1: T).(\lambda (v2:
-T).(\lambda (d1: C).(\lambda (v0: T).(\lambda (H2: (clear (CHead c3 (Flat f1)
-v1) (CHead d1 (Bind Void) v0))).(let H_x \def (H1 d1 v0 (clear_gen_flat f1 c3
-(CHead d1 (Bind Void) v0) v1 H2)) in (let H3 \def H_x in (ex2_2_ind C T
-(\lambda (d2: C).(\lambda (_: T).(csubv d1 d2))) (\lambda (d2: C).(\lambda
-(v3: T).(clear c4 (CHead d2 (Bind Void) v3)))) (ex2_2 C T (\lambda (d2:
-C).(\lambda (_: T).(csubv d1 d2))) (\lambda (d2: C).(\lambda (v3: T).(clear
-(CHead c4 (Flat f2) v2) (CHead d2 (Bind Void) v3))))) (\lambda (x0:
-C).(\lambda (x1: T).(\lambda (H4: (csubv d1 x0)).(\lambda (H5: (clear c4
-(CHead x0 (Bind Void) x1))).(ex2_2_intro C T (\lambda (d2: C).(\lambda (_:
-T).(csubv d1 d2))) (\lambda (d2: C).(\lambda (v3: T).(clear (CHead c4 (Flat
-f2) v2) (CHead d2 (Bind Void) v3)))) x0 x1 H4 (clear_flat c4 (CHead x0 (Bind
-Void) x1) H5 f2 v2)))))) H3)))))))))))))) c1 c2 H))).
-
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