7 Fixpoint blt [m,n: nat] : bool := Cases n m of
10 | (S n) (S m) => (blt m n)
13 Section blt_props. (******************************************************)
15 Theorem lt_blt: (x,y:?) (lt y x) -> (blt y x) = true.
16 XElim x; [ Intros; Inversion H | XElim y; Simpl; XAuto ].
19 Theorem le_bge: (x,y:?) (le x y) -> (blt y x) = false.
20 XElim x; [ XAuto | XElim y; Intros; [ Inversion H0 | Simpl; XAuto ] ].
23 Theorem blt_lt: (x,y:?) (blt y x) = true -> (lt y x).
24 XElim x; [ Intros; Inversion H | XElim y; Simpl; XAuto ].
27 Theorem bge_le: (x,y:?) (blt y x) = false -> (le x y).
28 XElim x; [ XAuto | XElim y; Intros; [ Inversion H0 | Simpl; XAuto ] ].
33 Hints Resolve lt_blt le_bge : ltlc.