Definition CReal_opp (x : CReal) : CReal :=
{|
  seq := CReal_opp_seq x;
  scale := CReal_opp_scale x;
  cauchy := CReal_opp_cauchy x;
  bound := CReal_opp_bound x
|}.Notation "- x" := (CReal_opp x) : CReal_scope.Definition CReal_minus (x y : CReal) : CReal
  := CReal_plus x (CReal_opp y).Infix "-" := CReal_minus : CReal_scope.

Lemma CReal_plus_le_reg_r : forall x y z : CReal, y + x <= z + x -> y <= z.