Theorems · Theorem · commutative algebra
Fintype.prod_dvd_of_isRelPrime
∀ {α : Type u_2} {I : Type u_1} [inst : CommMonoid α] [DecompositionMonoid α] {z : α} {s : I → α} [inst_2 : Fintype I],
Pairwise (Function.onFun IsRelPrime s) → (∀ (i : I), s i ∣ z) → ∏ x, s x ∣ z- Defined in
- Mathlib.RingTheory.Coprime.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Function.onFunstatement and proof · cited by 570
- Pairwisestatement and proof · cited by 516
- IsRelPrimestatement and proof · cited by 136
- DecompositionMonoidstatement and proof · cited by 39
- Pairwise.set_pairwiseproof · cited by 18
- Finset.prod_dvd_of_isRelPrimeproof · cited by 3
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