{T : CRing} {f g : rng_localization $-> T} (p : f $o loc_in $== g $o loc_in) : f $== g. Proof. srapply rng_localization_ind. - exact p. - hnf; intros x H q. change (inverse_elem (f x) = inverse_elem (g x)). apply isinvertible_unique. exact q. - hnf; intros x y q r. lhs nrapply rng_homo_mult. rhs nrapply rng_homo_mult. f_ap. Defined.
Require Import Basics.Overture Basics.Trunc Basics.Tactics Colimits.Quotient