proposition: Lemma Qclose_neg@{} : forall e (x y : Q), close e x y <-> close e (- x) (- y).
proof: Proof. intros e x y;split;intros E;apply Qclose_alt in E;apply Qclose_alt. - rewrite <-(negate_plus_distr),Qabs_neg. trivial. - rewrite <-(negate_plus_distr),Qabs_neg in E. trivial. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.rationals HoTT.Classes.interfaces.orders HoTT.Classes.implementations.peano_naturals HoTT.Classes.implementations.natpair_integers HoTT.Classes.theory.groups HoTT.Classes.theory.integers HoTT.Classes.theory.dec_fields HoTT.Classes.orders.dec_fields HoTT.Classes.orders.sum HoTT.Classes.theory.rationals HoTT.Classes.orders.lattices HoTT.Classes.implementations.assume_rationals HoTT.Classes.tactics.ring_quote HoTT.Classes.tactics.ring_tac