Theorems · Theorem · group theory
dvd_and_not_dvd_iff
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [IsCancelMulZero α] {x y : α}, x ∣ y ∧ ¬y ∣ x ↔ DvdNotUnit x y- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- mul_assocproof · cited by 1,667
- IsUnitproof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- IsCancelMulZerostatement and proof · cited by 177
- mul_left_cancel₀proof · cited by 47
- DvdNotUnitstatement and proof · cited by 33
- isUnit_iff_dvd_oneproof · cited by 21
- isUnit_of_dvd_oneproof · cited by 18
Cited by2
Results whose statement or proof uses this declaration.
- Associates.dvdNotUnit_iff_ltproof · cited by 4
- Ideal.span_singleton_lt_span_singletonproof · cited by 4