End UnitRingTheory.
Arguments invrK {R}.
Arguments invr_inj {R} [x1 x2].
Section UnitRingMorphism.
Variables (R S : unitRingType) (f : {rmorphism R -> S}).

Lemma invrZ k x : k \in unit -> x \in unit -> (k *: x)^-1 = k^-1 *: x^-1.
Section ClosedPredicates.