Theorems · Theorem · number theory
not_isUnit_of_not_isUnit_dvd
∀ {α : Type u_1} [inst : CommMonoid α] {a b : α}, ¬IsUnit a → a ∣ b → ¬IsUnit b- Defined in
- Mathlib.Algebra.Divisibility.Units
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- IsUnitstatement and proof · cited by 1,602
- isUnit_of_dvd_unitproof · cited by 22
Cited by3
Results whose statement or proof uses this declaration.
- pow_injective_of_not_isUnitproof · cited by 2
- WfDvdMonoid.not_isUnit_iff_exists_factors_eqproof · cited by 2
- DivisorChain.exists_chain_of_prime_powproof · cited by 1