Theorems · Definition · group theory
DivisibleBy.div
{A : Type u_1} →
{α : Type u_2} → {inst : AddMonoid A} → {inst_1 : SMul α A} → {inst_2 : Zero α} → [self : DivisibleBy A α] → A → α → AThe division function
- Defined in
- Mathlib.GroupTheory.Divisible
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- DivisibleBy
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- DivisibleBystatement and proof · cited by 8
Cited by8
Results whose statement or proof uses this declaration.
- DivisibleBy.div_cancelstatement · cited by 4
- DivisibleBy.surjective_smulproof · cited by 2
- AddCircle.ergodic_zsmul_addproof · cited by 1
- Module.Baer.of_divisibleproof · cited by 1
- AddGroup.divisibleByIntOfDivisibleByNatproof · cited by 0
- AddGroup.divisibleByNatOfDivisibleByIntproof · cited by 0
- AddCommGroup.smul_top_eq_top_of_divisibleBy_intproof · cited by 0
- DivisibleBy.div_zerostatement · cited by 0