Theorems · Theorem · field theory
DivisionRing.div_eq_mul_inv
∀ {K : Type u_2} [self : DivisionRing K] (a b : K), a / b = a * b⁻¹a / b := a * b⁻¹
- Defined in
- Mathlib.Algebra.Field.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- DivisionRing
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.
- DivisionRingstatement and proof · cited by 1,062
- DivisionRing.toInvstatement · cited by 4
- DivisionRing.toDivstatement · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- fieldOfFiniteDimensionalproof · cited by 1
- Field.ofIsUnitOrEqZeroproof · cited by 0
- Function.Injective.fieldproof · cited by 0
- Fintype.fieldOfDomainproof · cited by 0