Qed.
#[global]
Instance Rops: (@Ring_ops R 0%R 1%R Rplus Rmult Rminus Ropp (@eq R)).
Defined.
#[global]
Instance Rri : (Ring (Ro:=Rops)).
constructor;
try (try apply Rsth;
try (unfold respectful, Proper; unfold equality; unfold eq_notation in *;
intros; try rewrite H; try rewrite H0; reflexivity)).
- exact Rplus_0_l.
- exact Rplus_comm.
- symmetry. apply Rplus_assoc.
- exact Rmult_1_l.
- exact Rmult_1_r.
- symmetry. apply Rmult_assoc.
- exact Rmult_plus_distr_r.
- intros; apply Rmult_plus_distr_l.
- exact Rplus_opp_r.
Defined.
Ltac extra_reify term ::=
lazymatch term with
| IZR ?z =>
lazymatch isZcst z with
| true => open_constr:(PEc z)
| false => open_constr:(tt)
end
| _ => open_constr:(tt)
end.

Lemma R_one_zero: 1%R <> 0%R.
discrR.