(* This file was automatically generated: do not edit *********************)
-include "Basic-1/csubst0/defs.ma".
+include "basic_1/csubst0/defs.ma".
-theorem csubst0_snd_bind:
+lemma csubst0_snd_bind:
\forall (b: B).(\forall (i: nat).(\forall (v: T).(\forall (u1: T).(\forall
(u2: T).((subst0 i v u1 u2) \to (\forall (c: C).(csubst0 (S i) v (CHead c
(Bind b) u1) (CHead c (Bind b) u2))))))))
b) i) (\lambda (n: nat).(csubst0 n v (CHead c (Bind b) u1) (CHead c (Bind b)
u2))) (csubst0_snd (Bind b) i v u1 u2 H c) (S i) (refl_equal nat (S
i))))))))).
-(* COMMENTS
-Initial nodes: 91
-END *)
-theorem csubst0_fst_bind:
+lemma csubst0_fst_bind:
\forall (b: B).(\forall (i: nat).(\forall (c1: C).(\forall (c2: C).(\forall
(v: T).((csubst0 i v c1 c2) \to (\forall (u: T).(csubst0 (S i) v (CHead c1
(Bind b) u) (CHead c2 (Bind b) u))))))))
(v: T).(\lambda (H: (csubst0 i v c1 c2)).(\lambda (u: T).(eq_ind nat (s (Bind
b) i) (\lambda (n: nat).(csubst0 n v (CHead c1 (Bind b) u) (CHead c2 (Bind b)
u))) (csubst0_fst (Bind b) i c1 c2 v H u) (S i) (refl_equal nat (S i))))))))).
-(* COMMENTS
-Initial nodes: 91
-END *)
theorem csubst0_both_bind:
\forall (b: B).(\forall (i: nat).(\forall (v: T).(\forall (u1: T).(\forall
nat).(csubst0 n v (CHead c1 (Bind b) u1) (CHead c2 (Bind b) u2)))
(csubst0_both (Bind b) i v u1 u2 H c1 c2 H0) (S i) (refl_equal nat (S
i))))))))))).
-(* COMMENTS
-Initial nodes: 107
-END *)