- some bugs fixed in the domain-based preorders on environments

[helm.git] / helm / software / matita / contribs / LAMBDA-TYPES / LambdaDelta-1 / flt / props.ma

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/flt/props.ma b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/flt/props.ma
index bdb5ccaa0c4dcef3b6bfec99953ba1e745386baf..e6e148647d2fe2402865fc7d03f02271f581962f 100644 (file)
--- a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/flt/props.ma
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/flt/props.ma
@@ -14,17 +14,17 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "flt/defs.ma".
+include "LambdaDelta-1/flt/defs.ma".
 
-include "C/props.ma".
+include "LambdaDelta-1/C/props.ma".
 
 theorem flt_thead_sx:
  \forall (k: K).(\forall (c: C).(\forall (u: T).(\forall (t: T).(flt c u c 
 (THead k u t)))))
 \def
  \lambda (_: K).(\lambda (c: C).(\lambda (u: T).(\lambda (t: 
-T).(plus_le_lt_compat (cweight c) (cweight c) (tweight u) (S (plus (tweight 
-u) (tweight t))) (le_n (cweight c)) (le_n_S (tweight u) (plus (tweight u) 
+T).(le_lt_plus_plus (cweight c) (cweight c) (tweight u) (S (plus (tweight u) 
+(tweight t))) (le_n (cweight c)) (le_n_S (tweight u) (plus (tweight u) 
 (tweight t)) (le_plus_l (tweight u) (tweight t))))))).
 
 theorem flt_thead_dx:
@@ -32,8 +32,8 @@ theorem flt_thead_dx:
 (THead k u t)))))
 \def
  \lambda (_: K).(\lambda (c: C).(\lambda (u: T).(\lambda (t: 
-T).(plus_le_lt_compat (cweight c) (cweight c) (tweight t) (S (plus (tweight 
-u) (tweight t))) (le_n (cweight c)) (le_n_S (tweight t) (plus (tweight u) 
+T).(le_lt_plus_plus (cweight c) (cweight c) (tweight t) (S (plus (tweight u) 
+(tweight t))) (le_n (cweight c)) (le_n_S (tweight t) (plus (tweight u) 
 (tweight t)) (le_plus_r (tweight u) (tweight t))))))).
 
 theorem flt_shift:
@@ -46,7 +46,7 @@ k u) t c (THead k u t)))))
 (plus (cweight c) (tweight u)) (tweight t)) (\lambda (n: nat).(lt (plus (plus 
 (cweight c) (tweight u)) (tweight t)) (S n))) (le_n (S (plus (plus (cweight 
 c) (tweight u)) (tweight t)))) (plus (cweight c) (plus (tweight u) (tweight 
-t))) (plus_assoc (cweight c) (tweight u) (tweight t))) (plus (cweight c) (S 
+t))) (plus_assoc_l (cweight c) (tweight u) (tweight t))) (plus (cweight c) (S 
 (plus (tweight u) (tweight t)))) (plus_n_Sm (cweight c) (plus (tweight u) 
 (tweight t))))))).
 
@@ -69,7 +69,7 @@ K).(\lambda (t2: T).(\lambda (_: nat).(le_lt_trans (plus (cweight c1)
 (eq_ind_r nat (plus (S O) (plus (cweight c2) (tweight t2))) (\lambda (n: 
 nat).(lt (cweight c2) n)) (le_lt_n_Sm (cweight c2) (plus (cweight c2) 
 (tweight t2)) (le_plus_l (cweight c2) (tweight t2))) (plus (plus (cweight c2) 
-(tweight t2)) (S O)) (plus_comm (plus (cweight c2) (tweight t2)) (S 
+(tweight t2)) (S O)) (plus_sym (plus (cweight c2) (tweight t2)) (S 
 O))))))))))).
 
 theorem flt_arith2:
@@ -81,8 +81,18 @@ c1 t1 (CHead c2 k2 t2) (TLRef j)))))))))
 (H: (lt (plus (cweight c1) (tweight t1)) (plus (cweight c2) (S O)))).(\lambda 
 (_: K).(\lambda (t2: T).(\lambda (_: nat).(lt_le_trans (plus (cweight c1) 
 (tweight t1)) (plus (cweight c2) (S O)) (plus (plus (cweight c2) (tweight 
-t2)) (S O)) H (plus_le_compat (cweight c2) (plus (cweight c2) (tweight t2)) 
-(S O) (S O) (le_plus_l (cweight c2) (tweight t2)) (le_n (S O))))))))))).
+t2)) (S O)) H (le_plus_plus (cweight c2) (plus (cweight c2) (tweight t2)) (S 
+O) (S O) (le_plus_l (cweight c2) (tweight t2)) (le_n (S O))))))))))).
+
+theorem flt_trans:
+ \forall (c1: C).(\forall (c2: C).(\forall (t1: T).(\forall (t2: T).((flt c1 
+t1 c2 t2) \to (\forall (c3: C).(\forall (t3: T).((flt c2 t2 c3 t3) \to (flt 
+c1 t1 c3 t3))))))))
+\def
+ \lambda (c1: C).(\lambda (c2: C).(\lambda (t1: T).(\lambda (t2: T).(\lambda 
+(H: (lt (fweight c1 t1) (fweight c2 t2))).(\lambda (c3: C).(\lambda (t3: 
+T).(\lambda (H0: (lt (fweight c2 t2) (fweight c3 t3))).(lt_trans (fweight c1 
+t1) (fweight c2 t2) (fweight c3 t3) H H0)))))))).
 
 theorem flt_wf__q_ind:
  \forall (P: ((C \to (T \to Prop)))).(((\forall (n: nat).((\lambda (P0: ((C