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Theorems · Theorem · number theory

UniqueFactorizationMonoid.moebius_one

∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α],
  UniqueFactorizationMonoid.moebius 1 = 1
Defined in
Mathlib.RingTheory.UniqueFactorizationDomain.Moebius
Cited by
2 results in Mathlib
Foundations
Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidWithZeroUniqueFactorizationMonoid
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Around this declaration

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

IsUnit.moebius_eq · cited by 0IsUnit.moebius_eqIsRelPrime.moebius_mul · cited by 0IsRelPrime.moebius_mulpow_zero · cited by 1094pow_zeroCommMonoidWithZero · cited by 913CommMonoidWithZeroMultiset.card · cited by 375Multiset.cardUniqueFactorizationMonoid · cited by 279UniqueFactorizationMonoidUniqueFactorizationMonoid.moebius · cited by 10UniqueFactorizationMonoid…Squarefree.moebius_eq · cited by 3Squarefree.moebius_eqUniqueFactorizationMonoid.factors_one · cited by 2UniqueFactorizationMonoid…UniqueFactorizationMonoid.moe…CITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.