update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / ground_1 / types / props.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_1/types/props.ma b/matita/matita/contribs/lambdadelta/ground_1/types/props.ma
index 1948116a6c62a0a22143c15711222cc0a32661bc..79919dc763b16dc08dfd994f94168efed4f702c0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_1/types/props.ma
+++ b/matita/matita/contribs/lambdadelta/ground_1/types/props.ma
@@ -16,18 +16,15 @@
 
 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_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)))))))))).
+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)))).