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 ef1f15a9630438400688257704963ffdf9632bf7..0c7cef6283ebb1ab51f50b1e212711a705130a66 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/llt/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/llt/props.ma
@@ -14,11 +14,11 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/llt/defs.ma".
+include "basic_1/llt/defs.ma".
 
-include "Basic-1/leq/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
@@ -33,11 +33,8 @@ a3))).(\lambda (a4: A).(\lambda (a5: A).(\lambda (_: (leq g a4 a5)).(\lambda
 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)))).
-(* COMMENTS
-Initial nodes: 189
-END *)
 
-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
@@ -45,9 +42,6 @@ theorem llt_repl:
 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)))))).
-(* COMMENTS
-Initial nodes: 61
-END *)
 
 theorem llt_trans:
  \forall (a1: A).(\forall (a2: A).(\forall (a3: A).((llt a1 a2) \to ((llt a2 
@@ -56,59 +50,16 @@ a3) \to (llt a1 a3)))))
  \lambda (a1: A).(\lambda (a2: A).(\lambda (a3: A).(\lambda (H: (lt (lweight 
 a1) (lweight a2))).(\lambda (H0: (lt (lweight a2) (lweight a3))).(lt_trans 
 (lweight a1) (lweight a2) (lweight a3) H H0))))).
-(* COMMENTS
-Initial nodes: 43
-END *)
 
-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).(le_n_S (lweight a1) (plus (lweight a1) 
 (lweight a2)) (le_plus_l (lweight a1) (lweight a2)))).
-(* COMMENTS
-Initial nodes: 29
-END *)
 
-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).(le_n_S (lweight a2) (plus (lweight a1) 
 (lweight a2)) (le_plus_r (lweight a1) (lweight a2)))).
-(* COMMENTS
-Initial nodes: 29
-END *)
-
-theorem llt_wf__q_ind:
- \forall (P: ((A \to Prop))).(((\forall (n: nat).((\lambda (P0: ((A \to 
-Prop))).(\lambda (n0: nat).(\forall (a: A).((eq nat (lweight a) n0) \to (P0 
-a))))) P n))) \to (\forall (a: A).(P a)))
-\def
- let Q \def (\lambda (P: ((A \to Prop))).(\lambda (n: nat).(\forall (a: 
-A).((eq nat (lweight a) n) \to (P a))))) in (\lambda (P: ((A \to 
-Prop))).(\lambda (H: ((\forall (n: nat).(\forall (a: A).((eq nat (lweight a) 
-n) \to (P a)))))).(\lambda (a: A).(H (lweight a) a (refl_equal nat (lweight 
-a)))))).
-(* COMMENTS
-Initial nodes: 61
-END *)
-
-theorem llt_wf_ind:
- \forall (P: ((A \to Prop))).(((\forall (a2: A).(((\forall (a1: A).((llt a1 
-a2) \to (P a1)))) \to (P a2)))) \to (\forall (a: A).(P a)))
-\def
- let Q \def (\lambda (P: ((A \to Prop))).(\lambda (n: nat).(\forall (a: 
-A).((eq nat (lweight a) n) \to (P a))))) in (\lambda (P: ((A \to 
-Prop))).(\lambda (H: ((\forall (a2: A).(((\forall (a1: A).((lt (lweight a1) 
-(lweight a2)) \to (P a1)))) \to (P a2))))).(\lambda (a: A).(llt_wf__q_ind 
-(\lambda (a0: A).(P a0)) (\lambda (n: nat).(lt_wf_ind n (Q (\lambda (a0: 
-A).(P a0))) (\lambda (n0: nat).(\lambda (H0: ((\forall (m: nat).((lt m n0) 
-\to (Q (\lambda (a0: A).(P a0)) m))))).(\lambda (a0: A).(\lambda (H1: (eq nat 
-(lweight a0) n0)).(let H2 \def (eq_ind_r nat n0 (\lambda (n1: nat).(\forall 
-(m: nat).((lt m n1) \to (\forall (a1: A).((eq nat (lweight a1) m) \to (P 
-a1)))))) H0 (lweight a0) H1) in (H a0 (\lambda (a1: A).(\lambda (H3: (lt 
-(lweight a1) (lweight a0))).(H2 (lweight a1) H3 a1 (refl_equal nat (lweight 
-a1))))))))))))) a)))).
-(* COMMENTS
-Initial nodes: 179
-END *)