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(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(*                              Le_lt_compl.v                               *)
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(* Author: Pierre Casteran.                                                 *)
(*    LABRI, URA CNRS 1304,                                                 *)
(*    Departement d'Informatique, Universite Bordeaux I,                    *)
(*    33405 Talence CEDEX,                                                  *)
(*    e-mail:  casteran@labri.u-bordeaux.fr                                 *)
(* This file gives some additionnal lemmas to the modules Le and Lt of the distribution: ($COQTH/ARITH/[Le,Lt] )  Please notice that some lemmas and proofs use the constants one,two,three,four declared in the "Constants" module *)
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Hint Immediate not_le_lt: arith.
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Hint Immediate not_lt_le: arith.

Lemma lt_not_lt : forall n p : nat, n < p -> ~ p < S n.