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Theorems · Theorem · commutative algebra

IsRelPrime.of_prod_left

∀ {α : Type u_1} {I : Type u_2} [inst : CommMonoid α] [DecompositionMonoid α] {x : α} {s : I → α} {t : Finset I},
  IsRelPrime (∏ i ∈ t, s i) x → ∀ i ∈ t, IsRelPrime (s i) x
Defined in
Mathlib.RingTheory.Coprime.Lemmas
Cited by
1 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidDecompositionMonoid
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Around this declaration

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

IsRelPrime.pow_left_iff · cited by 2IsRelPrime.pow_left_iffFinset · cited by 13712FinsetFinset.prod · cited by 2356Finset.prodCommMonoid · cited by 2264CommMonoidIsRelPrime · cited by 136IsRelPrimeDecompositionMonoid · cited by 39DecompositionMonoidIsRelPrime.prod_left_iff · cited by 2IsRelPrime.prod_left_iffIsRelPrime.of_prod_leftCITED BYCITES

Cites6

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Cited by1

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