Theorems · Theorem · number theory
isUnit_iff_dvd_one
∀ {α : Type u_1} [inst : CommMonoid α] {x : α}, IsUnit x ↔ x ∣ 1- Defined in
- Mathlib.Algebra.Divisibility.Units
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidstatement and proof · cited by 2,264
- mul_commproof · cited by 2,262
- IsUnitstatement and proof · cited by 1,602
- IsUnit.dvdproof · cited by 13
Cited by21
Results whose statement or proof uses this declaration.
- isUnit_of_dvd_unitproof · cited by 22
- isUnit_of_dvd_oneproof · cited by 18
- Ideal.span_singleton_eq_topproof · cited by 10
- Nat.eq_one_of_dvd_coprimesproof · cited by 8
- Ideal.isUnit_iffproof · cited by 7
- Polynomial.associated_content_mulproof · cited by 6
- IsRadical.squarefreeproof · cited by 6
- PadicInt.isUnit_iffproof · cited by 4
- DvdNotUnit.not_isUnitproof · cited by 3
- Zsqrtd.norm_eq_one_iffproof · cited by 3
- prime_factors_uniqueproof · cited by 3
- Polynomial.isUnit_iff_degree_eq_zeroproof · cited by 3