Theorems · Theorem · group theory
Commute.inv_mul_eq_inv_mul_iff_of_isUnit
∀ {M : Type u_1} [inst : DivisionMonoid M] {a b c d : M},
Commute b d → IsUnit b → IsUnit d → (b⁻¹ * a = d⁻¹ * c ↔ d * a = b * c)- Defined in
- Mathlib.Algebra.Group.Commute.Units
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- DivisionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- mul_assocproof · cited by 1,667
- IsUnitstatement and proof · cited by 1,602
- Commutestatement and proof · cited by 639
- DivisionMonoidstatement and proof · cited by 201
- Commute.symmproof · cited by 79
- IsUnit.mulproof · cited by 32
- IsUnit.mul_right_injproof · cited by 13
- Commute.left_commproof · cited by 9
- IsUnit.mul_inv_cancelproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Commute.inv_mul_eq_inv_mul_iffproof · cited by 0