update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_1/C/props.ma b/matita/matita/contribs/lambdadelta/basic_1/C/props.ma
index 1cbfa54149fd3256f96d5130a34c060906527262..dacd5482b5a7790561b96a422db6f3bd2ade9c93 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/C/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/C/props.ma
@@ -18,7 +18,7 @@ include "basic_1/C/fwd.ma".
 
 include "basic_1/T/props.ma".
 
-theorem cle_r:
+lemma cle_r:
  \forall (c: C).(cle c c)
 \def
  \lambda (c: C).(C_ind (\lambda (c0: C).(le (cweight c0) (cweight c0))) 
@@ -26,7 +26,7 @@ theorem cle_r:
 (cweight c0))).(\lambda (_: K).(\lambda (t: T).(le_n (plus (cweight c0) 
 (tweight t))))))) c).
 
-theorem cle_head:
+lemma cle_head:
  \forall (c1: C).(\forall (c2: C).((cle c1 c2) \to (\forall (u1: T).(\forall 
 (u2: T).((tle u1 u2) \to (\forall (k: K).(cle (CHead c1 k u1) (CHead c2 k 
 u2))))))))
@@ -36,7 +36,7 @@ c2))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (H0: (le (tweight u1)
 (tweight u2))).(\lambda (_: K).(le_plus_plus (cweight c1) (cweight c2) 
 (tweight u1) (tweight u2) H H0))))))).
 
-theorem cle_trans_head:
+lemma cle_trans_head:
  \forall (c1: C).(\forall (c2: C).((cle c1 c2) \to (\forall (k: K).(\forall 
 (u: T).(cle c1 (CHead c2 k u))))))
 \def
@@ -44,7 +44,7 @@ theorem cle_trans_head:
 c2))).(\lambda (_: K).(\lambda (u: T).(le_plus_trans (cweight c1) (cweight 
 c2) (tweight u) H))))).
 
-theorem clt_cong:
+lemma clt_cong:
  \forall (c: C).(\forall (d: C).((clt c d) \to (\forall (k: K).(\forall (t: 
 T).(clt (CHead c k t) (CHead d k t))))))
 \def
@@ -52,14 +52,14 @@ T).(clt (CHead c k t) (CHead d k t))))))
 d))).(\lambda (_: K).(\lambda (t: T).(lt_reg_r (cweight c) (cweight d) 
 (tweight t) H))))).
 
-theorem clt_head:
+lemma clt_head:
  \forall (k: K).(\forall (c: C).(\forall (u: T).(clt c (CHead c k u))))
 \def
  \lambda (_: K).(\lambda (c: C).(\lambda (u: T).(eq_ind_r nat (plus (cweight 
 c) O) (\lambda (n: nat).(lt n (plus (cweight c) (tweight u)))) (lt_reg_l O 
 (tweight u) (cweight c) (tweight_lt u)) (cweight c) (plus_n_O (cweight c))))).
 
-theorem chead_ctail:
+lemma chead_ctail:
  \forall (c: C).(\forall (t: T).(\forall (k: K).(ex_3 K C T (\lambda (h: 
 K).(\lambda (d: C).(\lambda (u: T).(eq C (CHead c k t) (CTail h u d))))))))
 \def
@@ -83,7 +83,7 @@ C).(\lambda (u: T).(eq C (CHead (CTail x0 x2 x1) k0 t0) (CTail h u d))))) x0
 (CHead x1 k0 t0) x2 (refl_equal C (CHead (CTail x0 x2 x1) k0 t0))) (CHead c0 
 k t) H1))))) H0))))))))) c).
 
-theorem clt_thead:
+lemma clt_thead:
  \forall (k: K).(\forall (u: T).(\forall (c: C).(clt c (CTail k u c))))
 \def
  \lambda (k: K).(\lambda (u: T).(\lambda (c: C).(C_ind (\lambda (c0: C).(clt 
@@ -91,7 +91,7 @@ c0 (CTail k u c0))) (\lambda (n: nat).(clt_head k (CSort n) u)) (\lambda (c0:
 C).(\lambda (H: (clt c0 (CTail k u c0))).(\lambda (k0: K).(\lambda (t: 
 T).(clt_cong c0 (CTail k u c0) H k0 t))))) c))).
 
-theorem c_tail_ind:
+lemma c_tail_ind:
  \forall (P: ((C \to Prop))).(((\forall (n: nat).(P (CSort n)))) \to 
 (((\forall (c: C).((P c) \to (\forall (k: K).(\forall (t: T).(P (CTail k t 
 c))))))) \to (\forall (c: C).(P c))))