Theorems · Theorem · group theory
mul_eq_left
∀ {M : Type u_4} [inst : Monoid M] [IsLeftCancelMul M] {a b : M}, a * b = a ↔ b = 1- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- MonoidIsLeftCancelMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- IsLeftCancelMulstatement and proof · cited by 51
- mul_left_cancel_iffproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- left_eq_mulproof · cited by 2
- Subgroup.leftTransversals.diff_selfproof · cited by 2
- pow_two_semiclosedproof · cited by 1
- conj_eq_one_iffproof · cited by 1
- Equiv.mul_swap_eq_iffproof · cited by 1
- div_eq_selfproof · cited by 0
- mul_ne_leftproof · cited by 0