update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / ground_1 / blt / props.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_1/blt/props.ma b/matita/matita/contribs/lambdadelta/ground_1/blt/props.ma
deleted file mode 100644 (file)
index 7a6c3f2..0000000
--- a/matita/matita/contribs/lambdadelta/ground_1/blt/props.ma
+++ /dev/null
@@ -1,90 +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 "ground_1/blt/defs.ma".
-
-lemma lt_blt:
- \forall (x: nat).(\forall (y: nat).((lt y x) \to (eq bool (blt y x) true)))
-\def
- \lambda (x: nat).(nat_ind (\lambda (n: nat).(\forall (y: nat).((lt y n) \to 
-(eq bool (blt y n) true)))) (\lambda (y: nat).(\lambda (H: (lt y O)).(let H0 
-\def (match H with [le_n \Rightarrow (\lambda (H0: (eq nat (S y) O)).(let H1 
-\def (eq_ind nat (S y) (\lambda (e: nat).(match e with [O \Rightarrow False | 
-(S _) \Rightarrow True])) I O H0) in (False_ind (eq bool (blt y O) true) 
-H1))) | (le_S m H0) \Rightarrow (\lambda (H1: (eq nat (S m) O)).((let H2 \def 
-(eq_ind nat (S m) (\lambda (e: nat).(match e with [O \Rightarrow False | (S 
-_) \Rightarrow True])) I O H1) in (False_ind ((le (S y) m) \to (eq bool (blt 
-y O) true)) H2)) H0))]) in (H0 (refl_equal nat O))))) (\lambda (n: 
-nat).(\lambda (H: ((\forall (y: nat).((lt y n) \to (eq bool (blt y n) 
-true))))).(\lambda (y: nat).(nat_ind (\lambda (n0: nat).((lt n0 (S n)) \to 
-(eq bool (blt n0 (S n)) true))) (\lambda (_: (lt O (S n))).(refl_equal bool 
-true)) (\lambda (n0: nat).(\lambda (_: (((lt n0 (S n)) \to (eq bool (match n0 
-with [O \Rightarrow true | (S m) \Rightarrow (blt m n)]) true)))).(\lambda 
-(H1: (lt (S n0) (S n))).(H n0 (le_S_n (S n0) n H1))))) y)))) x).
-
-lemma le_bge:
- \forall (x: nat).(\forall (y: nat).((le x y) \to (eq bool (blt y x) false)))
-\def
- \lambda (x: nat).(nat_ind (\lambda (n: nat).(\forall (y: nat).((le n y) \to 
-(eq bool (blt y n) false)))) (\lambda (y: nat).(\lambda (_: (le O 
-y)).(refl_equal bool false))) (\lambda (n: nat).(\lambda (H: ((\forall (y: 
-nat).((le n y) \to (eq bool (blt y n) false))))).(\lambda (y: nat).(nat_ind 
-(\lambda (n0: nat).((le (S n) n0) \to (eq bool (blt n0 (S n)) false))) 
-(\lambda (H0: (le (S n) O)).(let H1 \def (match H0 with [le_n \Rightarrow 
-(\lambda (H1: (eq nat (S n) O)).(let H2 \def (eq_ind nat (S n) (\lambda (e: 
-nat).(match e with [O \Rightarrow False | (S _) \Rightarrow True])) I O H1) 
-in (False_ind (eq bool (blt O (S n)) false) H2))) | (le_S m H1) \Rightarrow 
-(\lambda (H2: (eq nat (S m) O)).((let H3 \def (eq_ind nat (S m) (\lambda (e: 
-nat).(match e with [O \Rightarrow False | (S _) \Rightarrow True])) I O H2) 
-in (False_ind ((le (S n) m) \to (eq bool (blt O (S n)) false)) H3)) H1))]) in 
-(H1 (refl_equal nat O)))) (\lambda (n0: nat).(\lambda (_: (((le (S n) n0) \to 
-(eq bool (blt n0 (S n)) false)))).(\lambda (H1: (le (S n) (S n0))).(H n0 
-(le_S_n n n0 H1))))) y)))) x).
-
-lemma blt_lt:
- \forall (x: nat).(\forall (y: nat).((eq bool (blt y x) true) \to (lt y x)))
-\def
- \lambda (x: nat).(nat_ind (\lambda (n: nat).(\forall (y: nat).((eq bool (blt 
-y n) true) \to (lt y n)))) (\lambda (y: nat).(\lambda (H: (eq bool (blt y O) 
-true)).(let H0 \def (match H with [refl_equal \Rightarrow (\lambda (H0: (eq 
-bool (blt y O) true)).(let H1 \def (eq_ind bool (blt y O) (\lambda (e: 
-bool).(match e with [true \Rightarrow False | false \Rightarrow True])) I 
-true H0) in (False_ind (lt y O) H1)))]) in (H0 (refl_equal bool true))))) 
-(\lambda (n: nat).(\lambda (H: ((\forall (y: nat).((eq bool (blt y n) true) 
-\to (lt y n))))).(\lambda (y: nat).(nat_ind (\lambda (n0: nat).((eq bool (blt 
-n0 (S n)) true) \to (lt n0 (S n)))) (\lambda (_: (eq bool true true)).(le_S_n 
-(S O) (S n) (le_n_S (S O) (S n) (le_n_S O n (le_O_n n))))) (\lambda (n0: 
-nat).(\lambda (_: (((eq bool (match n0 with [O \Rightarrow true | (S m) 
-\Rightarrow (blt m n)]) true) \to (lt n0 (S n))))).(\lambda (H1: (eq bool 
-(blt n0 n) true)).(lt_n_S n0 n (H n0 H1))))) y)))) x).
-
-lemma bge_le:
- \forall (x: nat).(\forall (y: nat).((eq bool (blt y x) false) \to (le x y)))
-\def
- \lambda (x: nat).(nat_ind (\lambda (n: nat).(\forall (y: nat).((eq bool (blt 
-y n) false) \to (le n y)))) (\lambda (y: nat).(\lambda (_: (eq bool (blt y O) 
-false)).(le_O_n y))) (\lambda (n: nat).(\lambda (H: ((\forall (y: nat).((eq 
-bool (blt y n) false) \to (le n y))))).(\lambda (y: nat).(nat_ind (\lambda 
-(n0: nat).((eq bool (blt n0 (S n)) false) \to (le (S n) n0))) (\lambda (H0: 
-(eq bool (blt O (S n)) false)).(let H1 \def (match H0 with [refl_equal 
-\Rightarrow (\lambda (H1: (eq bool (blt O (S n)) false)).(let H2 \def (eq_ind 
-bool (blt O (S n)) (\lambda (e: bool).(match e with [true \Rightarrow True | 
-false \Rightarrow False])) I false H1) in (False_ind (le (S n) O) H2)))]) in 
-(H1 (refl_equal bool false)))) (\lambda (n0: nat).(\lambda (_: (((eq bool 
-(blt n0 (S n)) false) \to (le (S n) n0)))).(\lambda (H1: (eq bool (blt (S n0) 
-(S n)) false)).(le_S_n (S n) (S n0) (le_n_S (S n) (S n0) (le_n_S n n0 (H n0 
-H1))))))) y)))) x).
-