update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / pr1 / props.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/pr1/props.ma b/matita/matita/contribs/lambdadelta/basic_1/pr1/props.ma
index 0615bed96d335c5d6e7a0fcf70065fcff76efb90..97a5e45d8477121403ae1e09dd08f3752f3f5583 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/pr1/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/pr1/props.ma
@@ -14,22 +14,19 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/pr1/defs.ma".
+include "basic_1/pr1/fwd.ma".
 
-include "Basic-1/pr0/subst1.ma".
+include "basic_1/pr0/subst1.ma".
 
-include "Basic-1/subst1/props.ma".
+include "basic_1/subst1/props.ma".
 
-include "Basic-1/T/props.ma".
+include "basic_1/T/props.ma".
 
-theorem pr1_pr0:
+lemma pr1_pr0:
  \forall (t1: T).(\forall (t2: T).((pr0 t1 t2) \to (pr1 t1 t2)))
 \def
  \lambda (t1: T).(\lambda (t2: T).(\lambda (H: (pr0 t1 t2)).(pr1_sing t2 t1 H 
 t2 (pr1_refl t2)))).
-(* COMMENTS
-Initial nodes: 23
-END *)
 
 theorem pr1_t:
  \forall (t2: T).(\forall (t1: T).((pr1 t1 t2) \to (\forall (t3: T).((pr1 t2 
@@ -42,11 +39,8 @@ t3) \to (pr1 t1 t3)))))
 (_: (pr1 t0 t4)).(\lambda (H2: ((\forall (t5: T).((pr1 t4 t5) \to (pr1 t0 
 t5))))).(\lambda (t5: T).(\lambda (H3: (pr1 t4 t5)).(pr1_sing t0 t3 H0 t5 (H2 
 t5 H3)))))))))) t1 t2 H))).
-(* COMMENTS
-Initial nodes: 103
-END *)
 
-theorem pr1_head_1:
+lemma pr1_head_1:
  \forall (u1: T).(\forall (u2: T).((pr1 u1 u2) \to (\forall (t: T).(\forall 
 (k: K).(pr1 (THead k u1 t) (THead k u2 t))))))
 \def
@@ -57,11 +51,8 @@ t0 t) (THead k t1 t)))) (\lambda (t0: T).(pr1_refl (THead k t0 t))) (\lambda
 (_: (pr1 t2 t3)).(\lambda (H2: (pr1 (THead k t2 t) (THead k t3 t))).(pr1_sing 
 (THead k t2 t) (THead k t1 t) (pr0_comp t1 t2 H0 t t (pr0_refl t) k) (THead k 
 t3 t) H2))))))) u1 u2 H))))).
-(* COMMENTS
-Initial nodes: 137
-END *)
 
-theorem pr1_head_2:
+lemma pr1_head_2:
  \forall (t1: T).(\forall (t2: T).((pr1 t1 t2) \to (\forall (u: T).(\forall 
 (k: K).(pr1 (THead k u t1) (THead k u t2))))))
 \def
@@ -72,9 +63,6 @@ T).(\lambda (t3: T).(\lambda (H0: (pr0 t3 t0)).(\lambda (t4: T).(\lambda (_:
 (pr1 t0 t4)).(\lambda (H2: (pr1 (THead k u t0) (THead k u t4))).(pr1_sing 
 (THead k u t0) (THead k u t3) (pr0_comp u u (pr0_refl u) t3 t0 H0 k) (THead k 
 u t4) H2))))))) t1 t2 H))))).
-(* COMMENTS
-Initial nodes: 137
-END *)
 
 theorem pr1_comp:
  \forall (v: T).(\forall (w: T).((pr1 v w) \to (\forall (t: T).(\forall (u: 
@@ -95,11 +83,8 @@ t0)).(\lambda (t5: T).(\lambda (_: (pr1 t0 t5)).(\lambda (H6: (pr1 (THead k
 t1 t0) (THead k t3 t5))).(pr1_sing (THead k t1 t0) (THead k t1 t4) (pr0_comp 
 t1 t1 (pr0_refl t1) t4 t0 H4 k) (THead k t3 t5) H6))))))) t u H3))))))))))) v 
 w H))).
-(* COMMENTS
-Initial nodes: 273
-END *)
 
-theorem pr1_eta:
+lemma pr1_eta:
  \forall (w: T).(\forall (u: T).(let t \def (THead (Bind Abst) w u) in 
 (\forall (v: T).((pr1 v w) \to (pr1 (THead (Bind Abst) v (THead (Flat Appl) 
 (TLRef O) (lift (S O) O t))) t)))))
@@ -116,11 +101,8 @@ O)) (lift (S O) (S O) u) (lift (S O) (S O) u) (pr0_refl (lift (S O) (S O)
 u))) u (pr1_sing (THead (Bind Abbr) (TLRef O) (lift (S O) O u)) (THead (Bind 
 Abbr) (TLRef O) (lift (S O) (S O) u)) (pr0_delta1 (TLRef O) (TLRef O) 
 (pr0_refl (TLRef O)) (lift (S O) (S O) u) (lift (S O) (S O) u) (pr0_refl 
-(lift (S O) (S O) u)) (lift (S O) O u) (subst1_lift_S u O O (le_n O))) u 
+(lift (S O) (S O) u)) (lift (S O) O u) (subst1_lift_S u O O (le_O_n O))) u 
 (pr1_pr0 (THead (Bind Abbr) (TLRef O) (lift (S O) O u)) u (pr0_zeta Abbr 
 not_abbr_abst u u (pr0_refl u) (TLRef O))))) (Bind Abst)) (lift (S O) O 
 (THead (Bind Abst) w u)) (lift_bind Abst w u (S O) O)))))).
-(* COMMENTS
-Initial nodes: 463
-END *)