include "ground_1/types/defs.ma".
-theorem ex2_sym:
+lemma ex2_sym:
\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: 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)))).(let TMP_10 \def (\lambda (x: A).(P x)) in (let TMP_9 \def (\lambda (x:
-A).(Q x)) in (let TMP_7 \def (\lambda (x: A).(Q x)) in (let TMP_6 \def
-(\lambda (x: A).(P x)) in (let TMP_8 \def (ex2 A TMP_7 TMP_6) in (let TMP_5
-\def (\lambda (x: A).(\lambda (H0: (P x)).(\lambda (H1: (Q x)).(let TMP_4
-\def (\lambda (x0: A).(Q x0)) in (let TMP_3 \def (\lambda (x0: A).(P x0)) in
-(ex_intro2 A TMP_4 TMP_3 x H1 H0)))))) in (ex2_ind A TMP_10 TMP_9 TMP_8 TMP_5
-H)))))))))).
+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)))).