(* This file was automatically generated: do not edit *********************)
-include "Basic-1/aprem/fwd.ma".
+include "basic_1/aprem/fwd.ma".
-include "Basic-1/leq/defs.ma".
+include "basic_1/leq/fwd.ma".
-theorem aprem_repl:
+lemma aprem_repl:
\forall (g: G).(\forall (a1: A).(\forall (a2: A).((leq g a1 a2) \to (\forall
(i: nat).(\forall (b2: A).((aprem i a2 b2) \to (ex2 A (\lambda (b1: A).(leq g
b1 b2)) (\lambda (b1: A).(aprem i a1 b1)))))))))
A (\lambda (b1: A).(leq g b1 b2)) (\lambda (b1: A).(aprem (S i0) (AHead a0
a4) b1)) x H7 (aprem_succ a4 x i0 H8 a0))))) H6))))))) i H4)))))))))))) a1 a2
H)))).
-(* COMMENTS
-Initial nodes: 621
-END *)
-theorem aprem_asucc:
+lemma aprem_asucc:
\forall (g: G).(\forall (a1: A).(\forall (a2: A).(\forall (i: nat).((aprem i
a1 a2) \to (aprem i (asucc g a1) a2)))))
\def
(i0: nat).(\lambda (_: (aprem i0 a0 a)).(\lambda (H1: (aprem i0 (asucc g a0)
a)).(\lambda (a3: A).(aprem_succ (asucc g a0) a i0 H1 a3))))))) i a1 a2
H))))).
-(* COMMENTS
-Initial nodes: 101
-END *)