Theorems · Theorem · commutative algebra
pairwise_isRelPrime_iff_isRelPrime_prod
∀ {α : Type u_2} {I : Type u_1} [inst : CommMonoid α] [DecompositionMonoid α] {s : I → α} {t : Finset I}
[inst_2 : DecidableEq I],
Pairwise (Function.onFun IsRelPrime fun i => s ↑i) ↔ ∀ i ∈ t, IsRelPrime (s i) (∏ j ∈ t \ {i}, s j)- Defined in
- Mathlib.RingTheory.Coprime.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.prodstatement and proof · 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
- Finset.mem_singletonproof · cited by 103
- Finset.mem_sdiffproof · cited by 44
- DecompositionMonoidstatement and proof · cited by 39
- IsRelPrime.prod_right_iffproof · cited by 2
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