Theorems · Theorem · group theory
DivisibleBy.div_cancel
∀ {A : Type u_1} {α : Type u_2} {inst : AddMonoid A} {inst_1 : SMul α A} {inst_2 : Zero α} [self : DivisibleBy A α]
{n : α} (a : A), n ≠ 0 → n • DivisibleBy.div a n = a- Defined in
- Mathlib.GroupTheory.Divisible
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- DivisibleBy
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.
- AddMonoidstatement and proof · cited by 2,864
- DivisibleBystatement and proof · cited by 8
- DivisibleBy.divstatement · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- DivisibleBy.surjective_smulproof · cited by 2
- AddCircle.ergodic_zsmul_addproof · cited by 1
- Module.Baer.of_divisibleproof · cited by 1
- AddCommGroup.smul_top_eq_top_of_divisibleBy_intproof · cited by 0