(* This file was automatically generated: do not edit *********************)
+include "LambdaDelta-1/csubst0/props.ma".
+
include "LambdaDelta-1/csubst0/fwd.ma".
include "LambdaDelta-1/clear/fwd.ma".
(CHead x5 (Bind x3) x7) H15 f x0) H16 H17))))))))))) H13)) H12)))))))) k H1
H3) c2 H4)))))))) H2)) (csubst0_gen_head k c c2 t v (S i) H0)))))))))))) c1).
+theorem csubst0_clear_trans:
+ \forall (c1: C).(\forall (c2: C).(\forall (v: T).(\forall (i: nat).((csubst0
+i v c1 c2) \to (\forall (e2: C).((clear c2 e2) \to (or (clear c1 e2) (ex2 C
+(\lambda (e1: C).(csubst0 i v e1 e2)) (\lambda (e1: C).(clear c1 e1))))))))))
+\def
+ \lambda (c1: C).(\lambda (c2: C).(\lambda (v: T).(\lambda (i: nat).(\lambda
+(H: (csubst0 i v c1 c2)).(csubst0_ind (\lambda (n: nat).(\lambda (t:
+T).(\lambda (c: C).(\lambda (c0: C).(\forall (e2: C).((clear c0 e2) \to (or
+(clear c e2) (ex2 C (\lambda (e1: C).(csubst0 n t e1 e2)) (\lambda (e1:
+C).(clear c e1)))))))))) (\lambda (k: K).(\lambda (i0: nat).(\lambda (v0:
+T).(\lambda (u1: T).(\lambda (u2: T).(\lambda (H0: (subst0 i0 v0 u1
+u2)).(\lambda (c: C).(\lambda (e2: C).(\lambda (H1: (clear (CHead c k u2)
+e2)).(K_ind (\lambda (k0: K).((clear (CHead c k0 u2) e2) \to (or (clear
+(CHead c k0 u1) e2) (ex2 C (\lambda (e1: C).(csubst0 (s k0 i0) v0 e1 e2))
+(\lambda (e1: C).(clear (CHead c k0 u1) e1)))))) (\lambda (b: B).(\lambda
+(H2: (clear (CHead c (Bind b) u2) e2)).(eq_ind_r C (CHead c (Bind b) u2)
+(\lambda (c0: C).(or (clear (CHead c (Bind b) u1) c0) (ex2 C (\lambda (e1:
+C).(csubst0 (s (Bind b) i0) v0 e1 c0)) (\lambda (e1: C).(clear (CHead c (Bind
+b) u1) e1))))) (or_intror (clear (CHead c (Bind b) u1) (CHead c (Bind b) u2))
+(ex2 C (\lambda (e1: C).(csubst0 (S i0) v0 e1 (CHead c (Bind b) u2)))
+(\lambda (e1: C).(clear (CHead c (Bind b) u1) e1))) (ex_intro2 C (\lambda
+(e1: C).(csubst0 (S i0) v0 e1 (CHead c (Bind b) u2))) (\lambda (e1: C).(clear
+(CHead c (Bind b) u1) e1)) (CHead c (Bind b) u1) (csubst0_snd_bind b i0 v0 u1
+u2 H0 c) (clear_bind b c u1))) e2 (clear_gen_bind b c e2 u2 H2)))) (\lambda
+(f: F).(\lambda (H2: (clear (CHead c (Flat f) u2) e2)).(or_introl (clear
+(CHead c (Flat f) u1) e2) (ex2 C (\lambda (e1: C).(csubst0 i0 v0 e1 e2))
+(\lambda (e1: C).(clear (CHead c (Flat f) u1) e1))) (clear_flat c e2
+(clear_gen_flat f c e2 u2 H2) f u1)))) k H1)))))))))) (\lambda (k:
+K).(\lambda (i0: nat).(\lambda (c3: C).(\lambda (c4: C).(\lambda (v0:
+T).(\lambda (H0: (csubst0 i0 v0 c3 c4)).(\lambda (H1: ((\forall (e2:
+C).((clear c4 e2) \to (or (clear c3 e2) (ex2 C (\lambda (e1: C).(csubst0 i0
+v0 e1 e2)) (\lambda (e1: C).(clear c3 e1)))))))).(\lambda (u: T).(\lambda
+(e2: C).(\lambda (H2: (clear (CHead c4 k u) e2)).(K_ind (\lambda (k0:
+K).((clear (CHead c4 k0 u) e2) \to (or (clear (CHead c3 k0 u) e2) (ex2 C
+(\lambda (e1: C).(csubst0 (s k0 i0) v0 e1 e2)) (\lambda (e1: C).(clear (CHead
+c3 k0 u) e1)))))) (\lambda (b: B).(\lambda (H3: (clear (CHead c4 (Bind b) u)
+e2)).(eq_ind_r C (CHead c4 (Bind b) u) (\lambda (c: C).(or (clear (CHead c3
+(Bind b) u) c) (ex2 C (\lambda (e1: C).(csubst0 (s (Bind b) i0) v0 e1 c))
+(\lambda (e1: C).(clear (CHead c3 (Bind b) u) e1))))) (or_intror (clear
+(CHead c3 (Bind b) u) (CHead c4 (Bind b) u)) (ex2 C (\lambda (e1: C).(csubst0
+(S i0) v0 e1 (CHead c4 (Bind b) u))) (\lambda (e1: C).(clear (CHead c3 (Bind
+b) u) e1))) (ex_intro2 C (\lambda (e1: C).(csubst0 (S i0) v0 e1 (CHead c4
+(Bind b) u))) (\lambda (e1: C).(clear (CHead c3 (Bind b) u) e1)) (CHead c3
+(Bind b) u) (csubst0_fst_bind b i0 c3 c4 v0 H0 u) (clear_bind b c3 u))) e2
+(clear_gen_bind b c4 e2 u H3)))) (\lambda (f: F).(\lambda (H3: (clear (CHead
+c4 (Flat f) u) e2)).(let H_x \def (H1 e2 (clear_gen_flat f c4 e2 u H3)) in
+(let H4 \def H_x in (or_ind (clear c3 e2) (ex2 C (\lambda (e1: C).(csubst0 i0
+v0 e1 e2)) (\lambda (e1: C).(clear c3 e1))) (or (clear (CHead c3 (Flat f) u)
+e2) (ex2 C (\lambda (e1: C).(csubst0 i0 v0 e1 e2)) (\lambda (e1: C).(clear
+(CHead c3 (Flat f) u) e1)))) (\lambda (H5: (clear c3 e2)).(or_introl (clear
+(CHead c3 (Flat f) u) e2) (ex2 C (\lambda (e1: C).(csubst0 i0 v0 e1 e2))
+(\lambda (e1: C).(clear (CHead c3 (Flat f) u) e1))) (clear_flat c3 e2 H5 f
+u))) (\lambda (H5: (ex2 C (\lambda (e1: C).(csubst0 i0 v0 e1 e2)) (\lambda
+(e1: C).(clear c3 e1)))).(ex2_ind C (\lambda (e1: C).(csubst0 i0 v0 e1 e2))
+(\lambda (e1: C).(clear c3 e1)) (or (clear (CHead c3 (Flat f) u) e2) (ex2 C
+(\lambda (e1: C).(csubst0 i0 v0 e1 e2)) (\lambda (e1: C).(clear (CHead c3
+(Flat f) u) e1)))) (\lambda (x: C).(\lambda (H6: (csubst0 i0 v0 x
+e2)).(\lambda (H7: (clear c3 x)).(or_intror (clear (CHead c3 (Flat f) u) e2)
+(ex2 C (\lambda (e1: C).(csubst0 i0 v0 e1 e2)) (\lambda (e1: C).(clear (CHead
+c3 (Flat f) u) e1))) (ex_intro2 C (\lambda (e1: C).(csubst0 i0 v0 e1 e2))
+(\lambda (e1: C).(clear (CHead c3 (Flat f) u) e1)) x H6 (clear_flat c3 x H7 f
+u)))))) H5)) H4))))) k H2))))))))))) (\lambda (k: K).(\lambda (i0:
+nat).(\lambda (v0: T).(\lambda (u1: T).(\lambda (u2: T).(\lambda (H0: (subst0
+i0 v0 u1 u2)).(\lambda (c3: C).(\lambda (c4: C).(\lambda (H1: (csubst0 i0 v0
+c3 c4)).(\lambda (H2: ((\forall (e2: C).((clear c4 e2) \to (or (clear c3 e2)
+(ex2 C (\lambda (e1: C).(csubst0 i0 v0 e1 e2)) (\lambda (e1: C).(clear c3
+e1)))))))).(\lambda (e2: C).(\lambda (H3: (clear (CHead c4 k u2) e2)).(K_ind
+(\lambda (k0: K).((clear (CHead c4 k0 u2) e2) \to (or (clear (CHead c3 k0 u1)
+e2) (ex2 C (\lambda (e1: C).(csubst0 (s k0 i0) v0 e1 e2)) (\lambda (e1:
+C).(clear (CHead c3 k0 u1) e1)))))) (\lambda (b: B).(\lambda (H4: (clear
+(CHead c4 (Bind b) u2) e2)).(eq_ind_r C (CHead c4 (Bind b) u2) (\lambda (c:
+C).(or (clear (CHead c3 (Bind b) u1) c) (ex2 C (\lambda (e1: C).(csubst0 (s
+(Bind b) i0) v0 e1 c)) (\lambda (e1: C).(clear (CHead c3 (Bind b) u1) e1)))))
+(or_intror (clear (CHead c3 (Bind b) u1) (CHead c4 (Bind b) u2)) (ex2 C
+(\lambda (e1: C).(csubst0 (S i0) v0 e1 (CHead c4 (Bind b) u2))) (\lambda (e1:
+C).(clear (CHead c3 (Bind b) u1) e1))) (ex_intro2 C (\lambda (e1: C).(csubst0
+(S i0) v0 e1 (CHead c4 (Bind b) u2))) (\lambda (e1: C).(clear (CHead c3 (Bind
+b) u1) e1)) (CHead c3 (Bind b) u1) (csubst0_both_bind b i0 v0 u1 u2 H0 c3 c4
+H1) (clear_bind b c3 u1))) e2 (clear_gen_bind b c4 e2 u2 H4)))) (\lambda (f:
+F).(\lambda (H4: (clear (CHead c4 (Flat f) u2) e2)).(let H_x \def (H2 e2
+(clear_gen_flat f c4 e2 u2 H4)) in (let H5 \def H_x in (or_ind (clear c3 e2)
+(ex2 C (\lambda (e1: C).(csubst0 i0 v0 e1 e2)) (\lambda (e1: C).(clear c3
+e1))) (or (clear (CHead c3 (Flat f) u1) e2) (ex2 C (\lambda (e1: C).(csubst0
+i0 v0 e1 e2)) (\lambda (e1: C).(clear (CHead c3 (Flat f) u1) e1)))) (\lambda
+(H6: (clear c3 e2)).(or_introl (clear (CHead c3 (Flat f) u1) e2) (ex2 C
+(\lambda (e1: C).(csubst0 i0 v0 e1 e2)) (\lambda (e1: C).(clear (CHead c3
+(Flat f) u1) e1))) (clear_flat c3 e2 H6 f u1))) (\lambda (H6: (ex2 C (\lambda
+(e1: C).(csubst0 i0 v0 e1 e2)) (\lambda (e1: C).(clear c3 e1)))).(ex2_ind C
+(\lambda (e1: C).(csubst0 i0 v0 e1 e2)) (\lambda (e1: C).(clear c3 e1)) (or
+(clear (CHead c3 (Flat f) u1) e2) (ex2 C (\lambda (e1: C).(csubst0 i0 v0 e1
+e2)) (\lambda (e1: C).(clear (CHead c3 (Flat f) u1) e1)))) (\lambda (x:
+C).(\lambda (H7: (csubst0 i0 v0 x e2)).(\lambda (H8: (clear c3 x)).(or_intror
+(clear (CHead c3 (Flat f) u1) e2) (ex2 C (\lambda (e1: C).(csubst0 i0 v0 e1
+e2)) (\lambda (e1: C).(clear (CHead c3 (Flat f) u1) e1))) (ex_intro2 C
+(\lambda (e1: C).(csubst0 i0 v0 e1 e2)) (\lambda (e1: C).(clear (CHead c3
+(Flat f) u1) e1)) x H7 (clear_flat c3 x H8 f u1)))))) H6)) H5))))) k
+H3))))))))))))) i v c1 c2 H))))).
+
projects / helm.git / blobdiff