proposition: Lemma two_fourth_is_one_half@{} : 2/4 = 1/2 :> Q+.
proof: Proof. assert (Hrw : 4 = 2 * 2 :> Q) by ring_tac.ring_with_nat. apply pos_eq. repeat (unfold cast;simpl). rewrite Hrw;clear Hrw. rewrite dec_recip_distr. rewrite mult_assoc. rewrite dec_recip_inverse;[|solve_propholds]. reflexivity. Unshelve. exact (fun _ => 1). 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