(* This file was automatically generated: do not edit *********************)
-include "LambdaDelta-1/aprem/defs.ma".
+include "Basic-1/aprem/defs.ma".
theorem aprem_gen_sort:
\forall (x: A).(\forall (i: nat).(\forall (h: nat).(\forall (n: nat).((aprem
in A return (\lambda (_: A).Prop) with [(ASort _ _) \Rightarrow False |
(AHead _ _) \Rightarrow True])) I (ASort h n) H3) in (False_ind False
H4))))))))) i y x H0))) H))))).
+(* COMMENTS
+Initial nodes: 227
+END *)
theorem aprem_gen_head_O:
\forall (a1: A).(\forall (a2: A).(\forall (x: A).((aprem O (AHead a1 a2) x)
(\lambda (ee: nat).(match ee in nat return (\lambda (_: nat).Prop) with [O
\Rightarrow False | (S _) \Rightarrow True])) I O H4) in (False_ind (eq A a
a1) H11)))))) H6)))))))))) y0 y x H1))) H0))) H)))).
+(* COMMENTS
+Initial nodes: 500
+END *)
theorem aprem_gen_head_S:
\forall (a1: A).(\forall (a2: A).(\forall (x: A).(\forall (i: nat).((aprem
(S i)) \to ((eq A a2 (AHead a1 a2)) \to (aprem i a2 a)))) H9 i H11) in (let
H13 \def (eq_ind nat i0 (\lambda (n: nat).(aprem n a2 a)) H10 i H11) in
H13))))))) H6)))))))))) y0 y x H1))) H0))) H))))).
+(* COMMENTS
+Initial nodes: 631
+END *)