two_fourth_is_one_half@{} : 2/4 = 1/2 :> Q+. 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.
Require Import Import Quoting.Instances. Import NatPair.Instances.