Qed.
(*Simplification rules missing in R *)
Hint Resolve Rabs_pos: real.

Theorem Rlt_Rminus_ZERO : forall r1 r2 : R, (r2 < r1)%R -> (0 < r1 - r2)%R.
intros r1 r2 H; replace 0%R with (r1 - r1)%R; unfold Rminus in |- *;
auto with real.