update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_1/pc1/props.ma b/matita/matita/contribs/lambdadelta/basic_1/pc1/props.ma
index 0da1a5aca058314aacc0badb603b5b7190819ce6..86e794a79c5771b62b45f6495a8b027dd781216a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/pc1/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/pc1/props.ma
@@ -14,40 +14,31 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/pc1/defs.ma".
+include "basic_1/pc1/defs.ma".
 
-include "Basic-1/pr1/pr1.ma".
+include "basic_1/pr1/pr1.ma".
 
-theorem pc1_pr0_r:
+lemma pc1_pr0_r:
  \forall (t1: T).(\forall (t2: T).((pr0 t1 t2) \to (pc1 t1 t2)))
 \def
  \lambda (t1: T).(\lambda (t2: T).(\lambda (H: (pr0 t1 t2)).(ex_intro2 T 
 (\lambda (t: T).(pr1 t1 t)) (\lambda (t: T).(pr1 t2 t)) t2 (pr1_pr0 t1 t2 H) 
 (pr1_refl t2)))).
-(* COMMENTS
-Initial nodes: 43
-END *)
 
-theorem pc1_pr0_x:
+lemma pc1_pr0_x:
  \forall (t1: T).(\forall (t2: T).((pr0 t2 t1) \to (pc1 t1 t2)))
 \def
  \lambda (t1: T).(\lambda (t2: T).(\lambda (H: (pr0 t2 t1)).(ex_intro2 T 
 (\lambda (t: T).(pr1 t1 t)) (\lambda (t: T).(pr1 t2 t)) t1 (pr1_refl t1) 
 (pr1_pr0 t2 t1 H)))).
-(* COMMENTS
-Initial nodes: 43
-END *)
 
-theorem pc1_refl:
+lemma pc1_refl:
  \forall (t: T).(pc1 t t)
 \def
  \lambda (t: T).(ex_intro2 T (\lambda (t0: T).(pr1 t t0)) (\lambda (t0: 
 T).(pr1 t t0)) t (pr1_refl t) (pr1_refl t)).
-(* COMMENTS
-Initial nodes: 31
-END *)
 
-theorem pc1_pr0_u:
+lemma pc1_pr0_u:
  \forall (t2: T).(\forall (t1: T).((pr0 t1 t2) \to (\forall (t3: T).((pc1 t2 
 t3) \to (pc1 t1 t3)))))
 \def
@@ -57,11 +48,8 @@ T).(pr1 t2 t)) (\lambda (t: T).(pr1 t3 t)) (pc1 t1 t3) (\lambda (x:
 T).(\lambda (H2: (pr1 t2 x)).(\lambda (H3: (pr1 t3 x)).(ex_intro2 T (\lambda 
 (t: T).(pr1 t1 t)) (\lambda (t: T).(pr1 t3 t)) x (pr1_sing t2 t1 H x H2) 
 H3)))) H1)))))).
-(* COMMENTS
-Initial nodes: 97
-END *)
 
-theorem pc1_s:
+lemma pc1_s:
  \forall (t2: T).(\forall (t1: T).((pc1 t1 t2) \to (pc1 t2 t1)))
 \def
  \lambda (t2: T).(\lambda (t1: T).(\lambda (H: (pc1 t1 t2)).(let H0 \def H in 
@@ -69,11 +57,8 @@ theorem pc1_s:
 t1) (\lambda (x: T).(\lambda (H1: (pr1 t1 x)).(\lambda (H2: (pr1 t2 
 x)).(ex_intro2 T (\lambda (t: T).(pr1 t2 t)) (\lambda (t: T).(pr1 t1 t)) x H2 
 H1)))) H0)))).
-(* COMMENTS
-Initial nodes: 79
-END *)
 
-theorem pc1_head_1:
+lemma pc1_head_1:
  \forall (u1: T).(\forall (u2: T).((pc1 u1 u2) \to (\forall (t: T).(\forall 
 (k: K).(pc1 (THead k u1 t) (THead k u2 t))))))
 \def
@@ -84,11 +69,8 @@ T).(\lambda (k: K).(let H0 \def H in (ex2_ind T (\lambda (t0: T).(pr1 u1 t0))
 (\lambda (t0: T).(pr1 (THead k u1 t) t0)) (\lambda (t0: T).(pr1 (THead k u2 
 t) t0)) (THead k x t) (pr1_head_1 u1 x H1 t k) (pr1_head_1 u2 x H2 t k))))) 
 H0)))))).
-(* COMMENTS
-Initial nodes: 133
-END *)
 
-theorem pc1_head_2:
+lemma pc1_head_2:
  \forall (t1: T).(\forall (t2: T).((pc1 t1 t2) \to (\forall (u: T).(\forall 
 (k: K).(pc1 (THead k u t1) (THead k u t2))))))
 \def
@@ -98,9 +80,6 @@ T).(\lambda (k: K).(let H0 \def H in (ex2_ind T (\lambda (t: T).(pr1 t1 t))
 T).(\lambda (H1: (pr1 t1 x)).(\lambda (H2: (pr1 t2 x)).(ex_intro2 T (\lambda 
 (t: T).(pr1 (THead k u t1) t)) (\lambda (t: T).(pr1 (THead k u t2) t)) (THead 
 k u x) (pr1_head_2 t1 x H1 u k) (pr1_head_2 t2 x H2 u k))))) H0)))))).
-(* COMMENTS
-Initial nodes: 133
-END *)
 
 theorem pc1_t:
  \forall (t2: T).(\forall (t1: T).((pc1 t1 t2) \to (\forall (t3: T).((pc1 t2 
@@ -117,19 +96,13 @@ t1 t3) (\lambda (x1: T).(\lambda (H7: (pr1 x0 x1)).(\lambda (H8: (pr1 x
 x1)).(ex_intro2 T (\lambda (t: T).(pr1 t1 t)) (\lambda (t: T).(pr1 t3 t)) x1 
 (pr1_t x0 t1 H5 x1 H7) (pr1_t x t3 H3 x1 H8))))) (pr1_confluence t2 x0 H6 x 
 H2))))) H4))))) H1)))))).
-(* COMMENTS
-Initial nodes: 203
-END *)
 
-theorem pc1_pr0_u2:
+lemma pc1_pr0_u2:
  \forall (t0: T).(\forall (t1: T).((pr0 t0 t1) \to (\forall (t2: T).((pc1 t0 
 t2) \to (pc1 t1 t2)))))
 \def
  \lambda (t0: T).(\lambda (t1: T).(\lambda (H: (pr0 t0 t1)).(\lambda (t2: 
 T).(\lambda (H0: (pc1 t0 t2)).(pc1_t t0 t1 (pc1_pr0_x t1 t0 H) t2 H0))))).
-(* COMMENTS
-Initial nodes: 35
-END *)
 
 theorem pc1_head:
  \forall (u1: T).(\forall (u2: T).((pc1 u1 u2) \to (\forall (t1: T).(\forall 
@@ -140,7 +113,4 @@ t2))))))))
 T).(\lambda (t2: T).(\lambda (H0: (pc1 t1 t2)).(\lambda (k: K).(pc1_t (THead 
 k u2 t1) (THead k u1 t1) (pc1_head_1 u1 u2 H t1 k) (THead k u2 t2) 
 (pc1_head_2 t1 t2 H0 u2 k)))))))).
-(* COMMENTS
-Initial nodes: 71
-END *)