(* This file was automatically generated: do not edit *********************)
-include "Ground-1/preamble.ma".
+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))))))
+lemma insert_eq:
+ \forall (S: Type[0]).(\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 *)
+ \lambda (S: Type[0]).(\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))))))).
-theorem unintro:
- \forall (A: Set).(\forall (a: A).(\forall (P: ((A \to Prop))).(((\forall (x:
-A).(P x))) \to (P a))))
+lemma unintro:
+ \forall (A: Type[0]).(\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 *)
+ \lambda (A: Type[0]).(\lambda (a: A).(\lambda (P: ((A \to Prop))).(\lambda
+(H: ((\forall (x: A).(P x)))).(H a)))).
-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))))
+lemma xinduction:
+ \forall (A: Type[0]).(\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 *)
+ \lambda (A: Type[0]).(\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))))).