update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / pc3 / pc1.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/pc3/pc1.ma b/matita/matita/contribs/lambdadelta/basic_1/pc3/pc1.ma
index 7093a13a1c7c53ad6980bd2ebc517ba0d173a97d..a629475c6f3ccd5515865b3e538b497922d92ce3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/pc3/pc1.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/pc3/pc1.ma
@@ -20,16 +20,14 @@ include "basic_1/pc1/defs.ma".
 
 include "basic_1/pr3/pr1.ma".
 
-theorem pc3_pc1:
+lemma pc3_pc1:
  \forall (t1: T).(\forall (t2: T).((pc1 t1 t2) \to (\forall (c: C).(pc3 c t1 
 t2))))
 \def
  \lambda (t1: T).(\lambda (t2: T).(\lambda (H: (pc1 t1 t2)).(\lambda (c: 
-C).(let H0 \def H in (let TMP_1 \def (\lambda (t: T).(pr1 t1 t)) in (let 
-TMP_2 \def (\lambda (t: T).(pr1 t2 t)) in (let TMP_3 \def (pc3 c t1 t2) in 
-(let TMP_8 \def (\lambda (x: T).(\lambda (H1: (pr1 t1 x)).(\lambda (H2: (pr1 
-t2 x)).(let TMP_4 \def (\lambda (t: T).(pr3 c t1 t)) in (let TMP_5 \def 
-(\lambda (t: T).(pr3 c t2 t)) in (let TMP_6 \def (pr3_pr1 t1 x H1 c) in (let 
-TMP_7 \def (pr3_pr1 t2 x H2 c) in (ex_intro2 T TMP_4 TMP_5 x TMP_6 
-TMP_7)))))))) in (ex2_ind T TMP_1 TMP_2 TMP_3 TMP_8 H0))))))))).
+C).(let H0 \def H in (ex2_ind T (\lambda (t: T).(pr1 t1 t)) (\lambda (t: 
+T).(pr1 t2 t)) (pc3 c t1 t2) (\lambda (x: T).(\lambda (H1: (pr1 t1 
+x)).(\lambda (H2: (pr1 t2 x)).(ex_intro2 T (\lambda (t: T).(pr3 c t1 t)) 
+(\lambda (t: T).(pr3 c t2 t)) x (pr3_pr1 t1 x H1 c) (pr3_pr1 t2 x H2 c))))) 
+H0))))).