proposition: Lemma Qabs_neg@{} : forall x : Q, abs (- x) = abs x.
proof: Proof. intros x. destruct (total_abs_either x) as [[E1 E2]|[E1 E2]]. - rewrite E2. path_via (- - x);[|rewrite involutive;trivial]. apply ((abs_sig (- x)).2). apply flip_nonneg_negate;trivial. - rewrite E2. apply ((abs_sig (- x)).2). apply flip_nonpos_negate;trivial. Qed.
imports: HoTT.Classes.implementations.peano_naturals HoTT.Classes.implementations.natpair_integers HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.naturals HoTT.Classes.interfaces.rationals HoTT.Classes.interfaces.orders HoTT.Classes.theory.groups HoTT.Classes.theory.integers HoTT.Classes.theory.dec_fields HoTT.Classes.orders.sum HoTT.Classes.orders.dec_fields HoTT.Classes.orders.lattices HoTT.Classes.theory.additional_operations HoTT.Classes.tactics.ring_quote HoTT.Classes.tactics.ring_tac