update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_1A / llt / props.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1A/llt/props.ma b/matita/matita/contribs/lambdadelta/basic_1A/llt/props.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+include "basic_1A/llt/defs.ma".
+
+include "basic_1A/leq/fwd.ma".
+
+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)).(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)))).
+
+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 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))).(lt_trans 
+(lweight a1) (lweight a2) (lweight a3) H H0))))).
+
+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)))).
+
+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)))).
+