Theorems · Theorem · group theory
Associates.dvdNotUnit_iff_lt
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [IsCancelMulZero M] {a b : Associates M}, DvdNotUnit a b ↔ a < b- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- Associatesstatement and proof · cited by 210
- IsCancelMulZerostatement and proof · cited by 177
- DvdNotUnitstatement · cited by 33
- dvd_and_not_dvd_iffproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- WfDvdMonoid.of_wellFoundedLT_associatesproof · cited by 1
- DivisorChain.element_of_chain_not_isUnit_of_index_ne_zeroproof · cited by 1
- DivisorChain.eq_second_of_chain_of_prime_dvdproof · cited by 1
- DivisorChain.exists_chain_of_prime_powproof · cited by 1