Theorems · Theorem · group theory
Units.eq_mul_inv_iff_mul_eq
∀ {α : Type u} [inst : Monoid α] (c : αˣ) {a b : α}, a = b * ↑c⁻¹ ↔ 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.
- IsUnit.eq_mul_inv_iff_mul_eqproof · cited by 2
- Associated.eq_zero_iffproof · cited by 2
- Matrix.isAdjointPair_equivproof · cited by 1
- spectrum.resolvent_sub_resolventproof · cited by 0
- Ideal.exists_mem_span_singleton_map_residueField_eqproof · cited by 0
- Polynomial.coeff_mem_radical_span_coeff_of_dvdproof · cited by 0