Theorems · Theorem · group theory
Commute.div_eq_div_iff_of_isUnit
∀ {M : Type u_1} [inst : DivisionMonoid M] {a b c d : M},
Commute b d → IsUnit b → IsUnit d → (a / b = c / d ↔ a * d = c * b)- Defined in
- Mathlib.Algebra.Group.Commute.Units
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- DivisionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- IsUnit.div_mul_cancelproof · cited by 37
- IsUnit.mulproof · cited by 32
- IsUnit.mul_left_injproof · cited by 20
- Commute.right_commproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Commute.div_eq_div_iffproof · cited by 2
- Commute.mul_inv_eq_mul_inv_iff_of_isUnitproof · cited by 1