refactoring of \lambda\delta version 1 in matita

[helm.git] / matitaB / matita / contribs / LAMBDA-TYPES / Basic-1 / llt / props.ma

diff --git a/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/llt/props.ma b/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/llt/props.ma
deleted file mode 100644 (file)
index ef1f15a..0000000
--- a/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/llt/props.ma
+++ /dev/null
@@ -1,114 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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-1/llt/defs.ma".
-
-include "Basic-1/leq/defs.ma".
-
-theorem 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)))).
-(* COMMENTS
-Initial nodes: 189
-END *)
-
-theorem 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)))))).
-(* COMMENTS
-Initial nodes: 61
-END *)
-
-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))))).
-(* COMMENTS
-Initial nodes: 43
-END *)
-
-theorem 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:
- \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 *)
-