Theorems · Theorem · group theory
Units.commute_iff_mul_inv_cancel
∀ {M : Type u_1} [inst : Monoid M] {u : Mˣ} {a : M}, Commute (↑u) a ↔ ↑u * a * ↑u⁻¹ = a- Defined in
- Mathlib.Algebra.Group.Commute.Units
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- 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
- Commutestatement and proof · cited by 639
- Units.mul_inv_eq_iff_eq_mulproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Units.commute_iff_mul_inv_cancel_assocproof · cited by 0
- commute_unitary_iff_star_right_conjugateproof · cited by 0