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Theorems · Theorem · commutative algebra

IsRegular.of_mul_left

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

If a product is regular, so is its left factor.

Defined in
Mathlib.Algebra.Regular.Basic
Cited by
2 results in Mathlib
Foundations
Depth 11 from the axioms · uses propext, Quot.sound
Assumes
CommSemigroup
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.IsHadamard.of_mul_conjTranspose · cited by 1IsHadamard.of_mul_conjTra…Matrix.IsHadamard.isRegular_det · cited by 0IsHadamard.isRegular_detIsRegular · cited by 116IsRegularCommSemigroup · cited by 62CommSemigroupisRegular_mul_iff · cited by 2isRegular_mul_iffIsRegular.of_mul_leftCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.