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15 (* This file was automatically generated: do not edit *********************)
17 include "basic_1A/csubst0/defs.ma".
19 lemma csubst0_snd_bind:
20 \forall (b: B).(\forall (i: nat).(\forall (v: T).(\forall (u1: T).(\forall
21 (u2: T).((subst0 i v u1 u2) \to (\forall (c: C).(csubst0 (S i) v (CHead c
22 (Bind b) u1) (CHead c (Bind b) u2))))))))
24 \lambda (b: B).(\lambda (i: nat).(\lambda (v: T).(\lambda (u1: T).(\lambda
25 (u2: T).(\lambda (H: (subst0 i v u1 u2)).(\lambda (c: C).(eq_ind nat (s (Bind
26 b) i) (\lambda (n: nat).(csubst0 n v (CHead c (Bind b) u1) (CHead c (Bind b)
27 u2))) (csubst0_snd (Bind b) i v u1 u2 H c) (S i) (refl_equal nat (S
30 lemma csubst0_fst_bind:
31 \forall (b: B).(\forall (i: nat).(\forall (c1: C).(\forall (c2: C).(\forall
32 (v: T).((csubst0 i v c1 c2) \to (\forall (u: T).(csubst0 (S i) v (CHead c1
33 (Bind b) u) (CHead c2 (Bind b) u))))))))
35 \lambda (b: B).(\lambda (i: nat).(\lambda (c1: C).(\lambda (c2: C).(\lambda
36 (v: T).(\lambda (H: (csubst0 i v c1 c2)).(\lambda (u: T).(eq_ind nat (s (Bind
37 b) i) (\lambda (n: nat).(csubst0 n v (CHead c1 (Bind b) u) (CHead c2 (Bind b)
38 u))) (csubst0_fst (Bind b) i c1 c2 v H u) (S i) (refl_equal nat (S i))))))))).
40 theorem csubst0_both_bind:
41 \forall (b: B).(\forall (i: nat).(\forall (v: T).(\forall (u1: T).(\forall
42 (u2: T).((subst0 i v u1 u2) \to (\forall (c1: C).(\forall (c2: C).((csubst0 i
43 v c1 c2) \to (csubst0 (S i) v (CHead c1 (Bind b) u1) (CHead c2 (Bind b)
46 \lambda (b: B).(\lambda (i: nat).(\lambda (v: T).(\lambda (u1: T).(\lambda
47 (u2: T).(\lambda (H: (subst0 i v u1 u2)).(\lambda (c1: C).(\lambda (c2:
48 C).(\lambda (H0: (csubst0 i v c1 c2)).(eq_ind nat (s (Bind b) i) (\lambda (n:
49 nat).(csubst0 n v (CHead c1 (Bind b) u1) (CHead c2 (Bind b) u2)))
50 (csubst0_both (Bind b) i v u1 u2 H c1 c2 H0) (S i) (refl_equal nat (S