proposition: Lemma pos_recip_r@{} : forall e : Q+, e / e = 1.
proof: Proof. intros;apply pos_eq. unfold dec_recip,cast,pos_recip;simpl. change (' e / ' e = 1). apply dec_recip_inverse. apply lt_ne_flip. solve_propholds. 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