proposition: Lemma CReal_plus_comm : forall x y : CReal, x + y == y + x.
proof: Proof. intros x y; apply CRealEq_diff; intros n. unfold CReal_plus, CReal_plus_seq. do 2 rewrite CReal_red_seq. do 2 rewrite Qred_correct. pose proof ((cauchy x) (n-1)%Z (n-1)%Z (n-1)%Z ltac:(lia) ltac:(lia)) as Hxbnd. pose proof ((cauchy y) (n-1)%Z (n-1)%Z (n-1)%Z ltac:(lia) ltac:(lia)) as Hybnd. apply Qlt_le_weak. rewrite Qabs_Qlt_condition in Hxbnd, Hybnd |- *. rewrite Qpower_minus_pos in Hxbnd, Hybnd. lra. Qed.
imports: QArith Qpower Qabs Qround Logic.ConstructiveEpsilon Lia Lqa QExtra ConstructiveExtra