X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FGround-1%2Fblt%2Fprops.ma;h=e5b569925b278ee909202b72717702fea052f366;hb=f538a0b46ba4164a21a76e47a6ed3b3e9deb5041;hp=751dcee9c59db4727038f5315f0b7f4269985b49;hpb=3531d88e2a19cba027b4b882f8dd74bf37283b9c;p=helm.git diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Ground-1/blt/props.ma b/helm/software/matita/contribs/LAMBDA-TYPES/Ground-1/blt/props.ma index 751dcee9c..e5b569925 100644 --- a/helm/software/matita/contribs/LAMBDA-TYPES/Ground-1/blt/props.ma +++ b/helm/software/matita/contribs/LAMBDA-TYPES/Ground-1/blt/props.ma @@ -14,7 +14,7 @@ (* This file was automatically generated: do not edit *********************) -include "Base-1/blt/defs.ma". +include "Ground-1/blt/defs.ma". theorem lt_blt: \forall (x: nat).(\forall (y: nat).((lt y x) \to (eq bool (blt y x) true))) @@ -37,6 +37,9 @@ 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). +(* COMMENTS +Initial nodes: 291 +END *) theorem le_bge: \forall (x: nat).(\forall (y: nat).((le x y) \to (eq bool (blt y x) false))) @@ -59,6 +62,9 @@ nat).(match e in nat return (\lambda (_: nat).Prop) with [O \Rightarrow False 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). +(* COMMENTS +Initial nodes: 293 +END *) theorem blt_lt: \forall (x: nat).(\forall (y: nat).((eq bool (blt y x) true) \to (lt y x))) @@ -78,6 +84,9 @@ 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). +(* COMMENTS +Initial nodes: 252 +END *) theorem bge_le: \forall (x: nat).(\forall (y: nat).((eq bool (blt y x) false) \to (le x y))) @@ -97,4 +106,7 @@ in bool return (\lambda (_: bool).Prop) with [true \Rightarrow True | false (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). +(* COMMENTS +Initial nodes: 262 +END *)