(****************************************************************************  IEEE754  :  Faux  Laurent Thery  ***************************************************************************** Auxillary properties about natural numbers, relative numbers and reals *)
Require Export Min.
Require Export Arith.
Require Export Reals.
Require Export Zpower.
Require Export ZArith.
Require Export Zcomplements.
Require Export sTactic.
Hint Resolve R1_neq_R0: real.
(*Missing rule for nat *)
intros a b H'.
apply sym_equal.
apply plus_minus; auto.
rewrite plus_comm; apply le_plus_minus; auto.
Qed.

Theorem lte_comp_mult :
forall p q r t : nat, p <= q -> r <= t -> p * r <= q * t.