Theorems · Theorem · commutative algebra

IsLeftRegular.of_mul

∀ {R : Type u_1} [inst : Semigroup R] {a b : R}, IsLeftRegular (a * b) → IsLeftRegular b

If an element b becomes left-regular after multiplying it on the left by a left-regular element, then b is left-regular.

Defined in

Mathlib.Algebra.Regular.Basic

Cited by

5 results in Mathlib

Foundations

Depth 7 from the axioms · uses propext, Quot.sound

Assumes

Semigroup