proposition: Lemma Qmeet_plus_l : forall a b c : Q, meet (a + b) (a + c) = a + meet b c.
proof: Proof. intros. destruct (total le b c) as [E|E]. - rewrite (meet_l _ _ E). apply meet_l. apply (order_preserving (a +)),E. - rewrite (meet_r _ _ E). apply meet_r. apply (order_preserving (a +)),E. 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