Theorems · Theorem · commutative algebra
IsLeftRegular.mul_left_eq_self_iff
∀ {R : Type u_1} [inst : Monoid R] {a b : R}, IsLeftRegular a → (a * b = a ↔ b = 1)- Defined in
- Mathlib.Algebra.Regular.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- mul_oneproof · cited by 3,885
- IsLeftRegularstatement and proof · cited by 97
Cited by1
Results whose statement or proof uses this declaration.
- IsLeftRegular.pow_injectiveproof · cited by 4