Theorems · Theorem · group theory
Units.mul_inv_eq_iff_eq_mul
∀ {α : Type u} [inst : Monoid α] (b : αˣ) {a c : α}, a * ↑b⁻¹ = c ↔ a = c * ↑b- Defined in
- Mathlib.Algebra.Group.Units.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- Units.mul_inv_cancel_rightproof · cited by 20
- Units.inv_mul_cancel_rightproof · cited by 9
Cited by6
Results whose statement or proof uses this declaration.
- isConj_iff_eqproof · cited by 3
- Units.commute_iff_mul_inv_cancelproof · cited by 2
- IsUnit.mul_inv_eq_iff_eq_mulproof · cited by 2
- MonoidHom.card_fiber_eq_of_mem_rangeproof · cited by 1
- Units.mul_liftRight_invproof · cited by 1
- Units.mul_inv_eq_mul_inv_iffproof · cited by 1