Theorems · Definition · group theory
DvdNotUnit
{α : Type u_1} → [CommMonoidWithZero α] → α → α → PropDvdNotUnit a b expresses that a divides b "strictly", i.e. that b divided by a
is not a unit.
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- CommMonoidWithZero
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.
- IsUnitproof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
Cited by36
Results whose statement or proof uses this declaration.
- WfDvdMonoidproof · cited by 37
- WfDvdMonoid.exists_irreducible_factorproof · cited by 12
- wellFounded_dvdNotUnitstatement · cited by 7
- WfDvdMonoid.induction_on_irreducibleproof · cited by 5
- dvdNotUnit_of_dvd_of_not_dvdstatement · cited by 4
- Associates.dvdNotUnit_iff_ltstatement · cited by 4
- Ideal.span_singleton_lt_span_singletonstatement and proof · cited by 4
- DvdNotUnit.not_isUnitstatement and proof · cited by 3
- Ideal.dvdNotUnit_iff_ltstatement and proof · cited by 3
- DvdNotUnit.isUnit_of_irreducible_rightstatement and proof · cited by 2
- IsBezout.TFAEproof · cited by 2
- WfDvdMonoid.max_power_factor'proof · cited by 2