1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
17 include "Base-1/preamble.ma".
20 \forall (S: Set).(\forall (x: S).(\forall (P: ((S \to Prop))).(\forall (G:
21 ((S \to Prop))).(((\forall (y: S).((P y) \to ((eq S y x) \to (G y))))) \to
24 \lambda (S: Set).(\lambda (x: S).(\lambda (P: ((S \to Prop))).(\lambda (G:
25 ((S \to Prop))).(\lambda (H: ((\forall (y: S).((P y) \to ((eq S y x) \to (G
26 y)))))).(\lambda (H0: (P x)).(H x H0 (refl_equal S x))))))).
29 \forall (A: Set).(\forall (a: A).(\forall (P: ((A \to Prop))).(((\forall (x:
30 A).(P x))) \to (P a))))
32 \lambda (A: Set).(\lambda (a: A).(\lambda (P: ((A \to Prop))).(\lambda (H:
33 ((\forall (x: A).(P x)))).(H a)))).
36 \forall (A: Set).(\forall (t: A).(\forall (P: ((A \to Prop))).(((\forall (x:
37 A).((eq A t x) \to (P x)))) \to (P t))))
39 \lambda (A: Set).(\lambda (t: A).(\lambda (P: ((A \to Prop))).(\lambda (H:
40 ((\forall (x: A).((eq A t x) \to (P x))))).(H t (refl_equal A t))))).