contribution about \lambda-\delta

[helm.git] / helm / coq-contribs / LAMBDA-TYPES / base_blt.v

diff --git a/helm/coq-contribs/LAMBDA-TYPES/base_blt.v b/helm/coq-contribs/LAMBDA-TYPES/base_blt.v
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+Require Arith.
+Require base_tactics.
+Require base_hints.
+
+(*#* #stop file *)
+
+      Fixpoint blt [m,n: nat] : bool := Cases n m of
+         | (0) m       => false
+         | (S n) (0)   => true
+         | (S n) (S m) => (blt m n)
+      end.
+
+   Section blt_props. (******************************************************)
+
+      Theorem lt_blt: (x,y:?) (lt y x) -> (blt y x) = true.
+      XElim x; [ Intros; Inversion H | XElim y; Simpl; XAuto ].
+      Qed.
+
+      Theorem le_bge: (x,y:?) (le x y) -> (blt y x) = false.
+      XElim x; [ XAuto | XElim y; Intros; [ Inversion H0 | Simpl; XAuto ] ].
+      Qed.
+
+      Theorem blt_lt: (x,y:?) (blt y x) = true -> (lt y x).
+      XElim x; [ Intros; Inversion H | XElim y; Simpl; XAuto ].
+      Qed.
+
+      Theorem bge_le: (x,y:?) (blt y x) = false -> (le x y).
+      XElim x; [ XAuto | XElim y; Intros; [ Inversion H0 | Simpl; XAuto ] ].
+      Qed.
+
+   End blt_props.
+
+      Hints Resolve lt_blt le_bge : ltlc.