Theorems · Theorem · group theory
left_eq_mul
∀ {M : Type u_4} [inst : Monoid M] [IsLeftCancelMul M] {a b : M}, a = a * b ↔ b = 1- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- MonoidIsLeftCancelMul
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
- IsLeftCancelMulstatement and proof · cited by 51
- mul_eq_leftproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.smul_diff'proof · cited by 2
- left_ne_mulproof · cited by 0