(* This file was automatically generated: do not edit *********************)
-include "Ground-1/types/defs.ma".
+include "ground_1/types/defs.ma".
theorem ex2_sym:
- \forall (A: Set).(\forall (P: ((A \to Prop))).(\forall (Q: ((A \to
+ \forall (A: Type[0]).(\forall (P: ((A \to Prop))).(\forall (Q: ((A \to
Prop))).((ex2 A (\lambda (x: A).(P x)) (\lambda (x: A).(Q x))) \to (ex2 A
(\lambda (x: A).(Q x)) (\lambda (x: A).(P x))))))
\def
- \lambda (A: Set).(\lambda (P: ((A \to Prop))).(\lambda (Q: ((A \to
+ \lambda (A: Type[0]).(\lambda (P: ((A \to Prop))).(\lambda (Q: ((A \to
Prop))).(\lambda (H: (ex2 A (\lambda (x: A).(P x)) (\lambda (x: A).(Q
-x)))).(ex2_ind A (\lambda (x: A).(P x)) (\lambda (x: A).(Q x)) (ex2 A
-(\lambda (x: A).(Q x)) (\lambda (x: A).(P x))) (\lambda (x: A).(\lambda (H0:
-(P x)).(\lambda (H1: (Q x)).(ex_intro2 A (\lambda (x0: A).(Q x0)) (\lambda
-(x0: A).(P x0)) x H1 H0)))) H)))).
-(* COMMENTS
-Initial nodes: 91
-END *)
+x)))).(let TMP_1 \def (\lambda (x: A).(P x)) in (let TMP_2 \def (\lambda (x:
+A).(Q x)) in (let TMP_3 \def (\lambda (x: A).(Q x)) in (let TMP_4 \def
+(\lambda (x: A).(P x)) in (let TMP_5 \def (ex2 A TMP_3 TMP_4) in (let TMP_8
+\def (\lambda (x: A).(\lambda (H0: (P x)).(\lambda (H1: (Q x)).(let TMP_6
+\def (\lambda (x0: A).(Q x0)) in (let TMP_7 \def (\lambda (x0: A).(P x0)) in
+(ex_intro2 A TMP_6 TMP_7 x H1 H0)))))) in (ex2_ind A TMP_1 TMP_2 TMP_5 TMP_8
+H)))))))))).