Mathlib Map

Theorems · Theorem · commutative algebra

IsRegular.mul

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

In a semigroup, the product of regular elements is regular.

Defined in
Mathlib.Algebra.Regular.Basic
Cited by
1 results in Mathlib
Foundations
Depth 8 from the axioms · uses propext, Quot.sound
Assumes
Semigroup
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

isRegular_mul_and_mul_iff · cited by 2isRegular_mul_and_mul_iffSemigroup · cited by 202SemigroupIsRegular · cited by 116IsRegularIsRegular.left · cited by 39IsRegular.leftIsRegular.right · cited by 19IsRegular.rightIsLeftRegular.mul · cited by 5IsLeftRegular.mulIsRightRegular.mul · cited by 3IsRightRegular.mulIsRegular.mulCITED BYCITES

Cites6

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

Cited by1

Results whose statement or proof uses this declaration.