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Theorems · Theorem · number theory

PNat.factorMultiset_mono

∀ {m n : ℕ+}, m ∣ n → m.factorMultiset ≤ n.factorMultiset

Alias of the reverse direction of PNat.factorMultiset_le_iff. We now have four different results that all encode the idea that inequality of multisets corresponds to divisibility of positive integers.

Defined in
Mathlib.Data.PNat.Factors
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Foundations
Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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PNat · cited by 392PNatPrimeMultiset · cited by 30PrimeMultisetPNat.factorMultiset · cited by 18PNat.factorMultisetPNat.factorMultiset_le_iff · cited by 5PNat.factorMultiset_le_iffPNat.factorMultiset_monoCITED BYCITES

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