--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+include "Ground-1/preamble.ma".
+
+theorem insert_eq:
+ \forall (S: Set).(\forall (x: S).(\forall (P: ((S \to Prop))).(\forall (G:
+((S \to Prop))).(((\forall (y: S).((P y) \to ((eq S y x) \to (G y))))) \to
+((P x) \to (G x))))))
+\def
+ \lambda (S: Set).(\lambda (x: S).(\lambda (P: ((S \to Prop))).(\lambda (G:
+((S \to Prop))).(\lambda (H: ((\forall (y: S).((P y) \to ((eq S y x) \to (G
+y)))))).(\lambda (H0: (P x)).(H x H0 (refl_equal S x))))))).
+(* COMMENTS
+Initial nodes: 45
+END *)
+
+theorem unintro:
+ \forall (A: Set).(\forall (a: A).(\forall (P: ((A \to Prop))).(((\forall (x:
+A).(P x))) \to (P a))))
+\def
+ \lambda (A: Set).(\lambda (a: A).(\lambda (P: ((A \to Prop))).(\lambda (H:
+((\forall (x: A).(P x)))).(H a)))).
+(* COMMENTS
+Initial nodes: 17
+END *)
+
+theorem xinduction:
+ \forall (A: Set).(\forall (t: A).(\forall (P: ((A \to Prop))).(((\forall (x:
+A).((eq A t x) \to (P x)))) \to (P t))))
+\def
+ \lambda (A: Set).(\lambda (t: A).(\lambda (P: ((A \to Prop))).(\lambda (H:
+((\forall (x: A).((eq A t x) \to (P x))))).(H t (refl_equal A t))))).
+(* COMMENTS
+Initial nodes: 31
+END *)
+