update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / pc3 / nf2.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/pc3/nf2.ma b/matita/matita/contribs/lambdadelta/basic_1/pc3/nf2.ma
index 9146795eb1834d1fbf3a62810f0cc47215b8bf48..3ce4180a14f7bf06632125510eb61690d32018e7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/pc3/nf2.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/pc3/nf2.ma
@@ -18,34 +18,29 @@ include "basic_1/pc3/defs.ma".
 
 include "basic_1/nf2/pr3.ma".
 
-theorem pc3_nf2:
+lemma pc3_nf2:
  \forall (c: C).(\forall (t1: T).(\forall (t2: T).((pc3 c t1 t2) \to ((nf2 c 
 t1) \to ((nf2 c t2) \to (eq T t1 t2))))))
 \def
  \lambda (c: C).(\lambda (t1: T).(\lambda (t2: T).(\lambda (H: (pc3 c t1 
 t2)).(\lambda (H0: (nf2 c t1)).(\lambda (H1: (nf2 c t2)).(let H2 \def H in 
-(let TMP_1 \def (\lambda (t: T).(pr3 c t1 t)) in (let TMP_2 \def (\lambda (t: 
-T).(pr3 c t2 t)) in (let TMP_3 \def (eq T t1 t2) in (let TMP_9 \def (\lambda 
-(x: T).(\lambda (H3: (pr3 c t1 x)).(\lambda (H4: (pr3 c t2 x)).(let H_y \def 
-(nf2_pr3_unfold c t1 x H3 H0) in (let TMP_4 \def (\lambda (t: T).(pr3 c t2 
-t)) in (let H5 \def (eq_ind_r T x TMP_4 H4 t1 H_y) in (let TMP_5 \def 
-(\lambda (t: T).(pr3 c t1 t)) in (let H6 \def (eq_ind_r T x TMP_5 H3 t1 H_y) 
-in (let H_y0 \def (nf2_pr3_unfold c t2 t1 H5 H1) in (let TMP_6 \def (\lambda 
-(t: T).(pr3 c t t1)) in (let H7 \def (eq_ind T t2 TMP_6 H5 t1 H_y0) in (let 
-TMP_7 \def (\lambda (t: T).(eq T t1 t)) in (let TMP_8 \def (refl_equal T t1) 
-in (eq_ind_r T t1 TMP_7 TMP_8 t2 H_y0)))))))))))))) in (ex2_ind T TMP_1 TMP_2 
-TMP_3 TMP_9 H2))))))))))).
+(ex2_ind T (\lambda (t: T).(pr3 c t1 t)) (\lambda (t: T).(pr3 c t2 t)) (eq T 
+t1 t2) (\lambda (x: T).(\lambda (H3: (pr3 c t1 x)).(\lambda (H4: (pr3 c t2 
+x)).(let H_y \def (nf2_pr3_unfold c t1 x H3 H0) in (let H5 \def (eq_ind_r T x 
+(\lambda (t: T).(pr3 c t2 t)) H4 t1 H_y) in (let H6 \def (eq_ind_r T x 
+(\lambda (t: T).(pr3 c t1 t)) H3 t1 H_y) in (let H_y0 \def (nf2_pr3_unfold c 
+t2 t1 H5 H1) in (let H7 \def (eq_ind T t2 (\lambda (t: T).(pr3 c t t1)) H5 t1 
+H_y0) in (eq_ind_r T t1 (\lambda (t: T).(eq T t1 t)) (refl_equal T t1) t2 
+H_y0))))))))) H2))))))).
 
-theorem pc3_nf2_unfold:
+lemma pc3_nf2_unfold:
  \forall (c: C).(\forall (t1: T).(\forall (t2: T).((pc3 c t1 t2) \to ((nf2 c 
 t2) \to (pr3 c t1 t2)))))
 \def
  \lambda (c: C).(\lambda (t1: T).(\lambda (t2: T).(\lambda (H: (pc3 c t1 
-t2)).(\lambda (H0: (nf2 c t2)).(let H1 \def H in (let TMP_1 \def (\lambda (t: 
-T).(pr3 c t1 t)) in (let TMP_2 \def (\lambda (t: T).(pr3 c t2 t)) in (let 
-TMP_3 \def (pr3 c t1 t2) in (let TMP_5 \def (\lambda (x: T).(\lambda (H2: 
-(pr3 c t1 x)).(\lambda (H3: (pr3 c t2 x)).(let H_y \def (nf2_pr3_unfold c t2 
-x H3 H0) in (let TMP_4 \def (\lambda (t: T).(pr3 c t1 t)) in (let H4 \def 
-(eq_ind_r T x TMP_4 H2 t2 H_y) in H4)))))) in (ex2_ind T TMP_1 TMP_2 TMP_3 
-TMP_5 H1)))))))))).
+t2)).(\lambda (H0: (nf2 c t2)).(let H1 \def H in (ex2_ind T (\lambda (t: 
+T).(pr3 c t1 t)) (\lambda (t: T).(pr3 c t2 t)) (pr3 c t1 t2) (\lambda (x: 
+T).(\lambda (H2: (pr3 c t1 x)).(\lambda (H3: (pr3 c t2 x)).(let H_y \def 
+(nf2_pr3_unfold c t2 x H3 H0) in (let H4 \def (eq_ind_r T x (\lambda (t: 
+T).(pr3 c t1 t)) H2 t2 H_y) in H4))))) H1)))))).