Theorems · Theorem · group theory
mul_eq_right
∀ {M : Type u_4} [inst : Monoid M] [IsRightCancelMul M] {a b : M}, a * b = b ↔ a = 1- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- MonoidIsRightCancelMul
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
- one_mulproof · cited by 2,841
- IsRightCancelMulstatement and proof · cited by 43
- mul_right_cancel_iffproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- right_eq_mulproof · cited by 2
- gaussSum_aux_of_mulShiftproof · cited by 1
- Equiv.swap_mul_eq_iffproof · cited by 0
- mul_ne_rightproof · cited by 0
- div_eq_inv_selfproof · cited by 0