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Theorems · Theorem · group theory

dvdNotUnit_of_dvd_of_not_dvd

∀ {α : Type u_1} [inst : CommMonoidWithZero α] {a b : α}, a ∣ b → ¬b ∣ a → DvdNotUnit a b
Defined in
Mathlib.Algebra.GroupWithZero.Divisibility
Cited by
4 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext
Assumes
CommMonoidWithZero
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Ideal.dvdNotUnit_iff_lt · cited by 3Ideal.dvdNotUnit_iff_ltUniqueFactorizationMonoid.dvdNotUnit_iff_normalizedFactors_lt_normalizedFactors · cited by 1UniqueFactorizationMonoid…Valuation.Integers.dvdNotUnit_iff_lt · cited by 1Integers.dvdNotUnit_iff_ltNat.dvdNotUnit_setGcd_insert · cited by 0Nat.dvdNotUnit_setGcd_ins…Units · cited by 2804UnitsUnits.val · cited by 1966Units.valIsUnit · cited by 1602IsUnitCommMonoidWithZero · cited by 913CommMonoidWithZerodvd_zero · cited by 63dvd_zeroDvdNotUnit · cited by 33DvdNotUnitdvdNotUnit_of_dvd_of_not_dvdCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.