Theorems · Theorem · group theory
GroupWithZero.div_eq_mul_inv
∀ {G₀ : Type u} [self : GroupWithZero G₀] (a b : G₀), a / b = a * b⁻¹a / b := a * b⁻¹
- Defined in
- Mathlib.Algebra.GroupWithZero.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- GroupWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- GroupWithZerostatement and proof · cited by 691
- GroupWithZero.toInvstatement · cited by 4
- GroupWithZero.toDivstatement · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- Fintype.divisionRingOfIsDomainproof · cited by 1
- Function.Injective.divisionSemiringproof · cited by 0
- commGroupWithZeroOfIsUnitOrEqZeroproof · cited by 0
- DivisionRing.ofIsUnitOrEqZeroproof · cited by 0
- Function.Surjective.commGroupWithZeroproof · cited by 0
- Function.Injective.divisionRingproof · cited by 0
- Function.Injective.commGroupWithZeroproof · cited by 0