update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_1/llt/props.ma b/matita/matita/contribs/lambdadelta/basic_1/llt/props.ma
index fb70372f938d8a4ac3b2bd0539ff0c7f82348765..0c7cef6283ebb1ab51f50b1e212711a705130a66 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/llt/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/llt/props.ma
@@ -18,63 +18,48 @@ include "basic_1/llt/defs.ma".
 
 include "basic_1/leq/fwd.ma".
 
-theorem lweight_repl:
+lemma lweight_repl:
  \forall (g: G).(\forall (a1: A).(\forall (a2: A).((leq g a1 a2) \to (eq nat 
 (lweight a1) (lweight a2)))))
 \def
  \lambda (g: G).(\lambda (a1: A).(\lambda (a2: A).(\lambda (H: (leq g a1 
-a2)).(let TMP_3 \def (\lambda (a: A).(\lambda (a0: A).(let TMP_1 \def 
-(lweight a) in (let TMP_2 \def (lweight a0) in (eq nat TMP_1 TMP_2))))) in 
-(let TMP_4 \def (\lambda (h1: nat).(\lambda (h2: nat).(\lambda (n1: 
-nat).(\lambda (n2: nat).(\lambda (k: nat).(\lambda (_: (eq A (aplus g (ASort 
-h1 n1) k) (aplus g (ASort h2 n2) k))).(refl_equal nat O))))))) in (let TMP_16 
-\def (\lambda (a0: A).(\lambda (a3: A).(\lambda (_: (leq g a0 a3)).(\lambda 
-(H1: (eq nat (lweight a0) (lweight a3))).(\lambda (a4: A).(\lambda (a5: 
-A).(\lambda (_: (leq g a4 a5)).(\lambda (H3: (eq nat (lweight a4) (lweight 
-a5))).(let TMP_5 \def (lweight a0) in (let TMP_6 \def (lweight a4) in (let 
-TMP_7 \def (plus TMP_5 TMP_6) in (let TMP_8 \def (lweight a3) in (let TMP_9 
-\def (lweight a5) in (let TMP_10 \def (plus TMP_8 TMP_9) in (let TMP_11 \def 
-(lweight a0) in (let TMP_12 \def (lweight a3) in (let TMP_13 \def (lweight 
-a4) in (let TMP_14 \def (lweight a5) in (let TMP_15 \def (f_equal2 nat nat 
-nat plus TMP_11 TMP_12 TMP_13 TMP_14 H1 H3) in (f_equal nat nat S TMP_7 
-TMP_10 TMP_15)))))))))))))))))))) in (leq_ind g TMP_3 TMP_4 TMP_16 a1 a2 
-H))))))).
+a2)).(leq_ind g (\lambda (a: A).(\lambda (a0: A).(eq nat (lweight a) (lweight 
+a0)))) (\lambda (h1: nat).(\lambda (h2: nat).(\lambda (n1: nat).(\lambda (n2: 
+nat).(\lambda (k: nat).(\lambda (_: (eq A (aplus g (ASort h1 n1) k) (aplus g 
+(ASort h2 n2) k))).(refl_equal nat O))))))) (\lambda (a0: A).(\lambda (a3: 
+A).(\lambda (_: (leq g a0 a3)).(\lambda (H1: (eq nat (lweight a0) (lweight 
+a3))).(\lambda (a4: A).(\lambda (a5: A).(\lambda (_: (leq g a4 a5)).(\lambda 
+(H3: (eq nat (lweight a4) (lweight a5))).(f_equal nat nat S (plus (lweight 
+a0) (lweight a4)) (plus (lweight a3) (lweight a5)) (f_equal2 nat nat nat plus 
+(lweight a0) (lweight a3) (lweight a4) (lweight a5) H1 H3)))))))))) a1 a2 
+H)))).
 
-theorem llt_repl:
+lemma llt_repl:
  \forall (g: G).(\forall (a1: A).(\forall (a2: A).((leq g a1 a2) \to (\forall 
 (a3: A).((llt a1 a3) \to (llt a2 a3))))))
 \def
  \lambda (g: G).(\lambda (a1: A).(\lambda (a2: A).(\lambda (H: (leq g a1 
-a2)).(\lambda (a3: A).(\lambda (H0: (lt (lweight a1) (lweight a3))).(let 
-TMP_1 \def (lweight a1) in (let TMP_3 \def (\lambda (n: nat).(let TMP_2 \def 
-(lweight a3) in (lt n TMP_2))) in (let TMP_4 \def (lweight a2) in (let TMP_5 
-\def (lweight_repl g a1 a2 H) in (let H1 \def (eq_ind nat TMP_1 TMP_3 H0 
-TMP_4 TMP_5) in H1)))))))))).
+a2)).(\lambda (a3: A).(\lambda (H0: (lt (lweight a1) (lweight a3))).(let H1 
+\def (eq_ind nat (lweight a1) (\lambda (n: nat).(lt n (lweight a3))) H0 
+(lweight a2) (lweight_repl g a1 a2 H)) in H1)))))).
 
 theorem llt_trans:
  \forall (a1: A).(\forall (a2: A).(\forall (a3: A).((llt a1 a2) \to ((llt a2 
 a3) \to (llt a1 a3)))))
 \def
  \lambda (a1: A).(\lambda (a2: A).(\lambda (a3: A).(\lambda (H: (lt (lweight 
-a1) (lweight a2))).(\lambda (H0: (lt (lweight a2) (lweight a3))).(let TMP_1 
-\def (lweight a1) in (let TMP_2 \def (lweight a2) in (let TMP_3 \def (lweight 
-a3) in (lt_trans TMP_1 TMP_2 TMP_3 H H0)))))))).
+a1) (lweight a2))).(\lambda (H0: (lt (lweight a2) (lweight a3))).(lt_trans 
+(lweight a1) (lweight a2) (lweight a3) H H0))))).
 
-theorem llt_head_sx:
+lemma llt_head_sx:
  \forall (a1: A).(\forall (a2: A).(llt a1 (AHead a1 a2)))
 \def
- \lambda (a1: A).(\lambda (a2: A).(let TMP_1 \def (lweight a1) in (let TMP_2 
-\def (lweight a1) in (let TMP_3 \def (lweight a2) in (let TMP_4 \def (plus 
-TMP_2 TMP_3) in (let TMP_5 \def (lweight a1) in (let TMP_6 \def (lweight a2) 
-in (let TMP_7 \def (le_plus_l TMP_5 TMP_6) in (le_n_S TMP_1 TMP_4 
-TMP_7))))))))).
+ \lambda (a1: A).(\lambda (a2: A).(le_n_S (lweight a1) (plus (lweight a1) 
+(lweight a2)) (le_plus_l (lweight a1) (lweight a2)))).
 
-theorem llt_head_dx:
+lemma llt_head_dx:
  \forall (a1: A).(\forall (a2: A).(llt a2 (AHead a1 a2)))
 \def
- \lambda (a1: A).(\lambda (a2: A).(let TMP_1 \def (lweight a2) in (let TMP_2 
-\def (lweight a1) in (let TMP_3 \def (lweight a2) in (let TMP_4 \def (plus 
-TMP_2 TMP_3) in (let TMP_5 \def (lweight a1) in (let TMP_6 \def (lweight a2) 
-in (let TMP_7 \def (le_plus_r TMP_5 TMP_6) in (le_n_S TMP_1 TMP_4 
-TMP_7))))))))).
+ \lambda (a1: A).(\lambda (a2: A).(le_n_S (lweight a2) (plus (lweight a1) 
+(lweight a2)) (le_plus_r (lweight a1) (lweight a2)))).