Theorems · Theorem · commutative algebra
IsRelPrime.prod_right
∀ {α : Type u_2} {I : Type u_1} [inst : CommMonoid α] [DecompositionMonoid α] {x : α} {s : I → α} {t : Finset I},
(∀ i ∈ t, IsRelPrime x (s i)) → IsRelPrime x (∏ i ∈ t, s i)- Defined in
- Mathlib.RingTheory.Coprime.Lemmas
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- IsRelPrimestatement · cited by 136
- DecompositionMonoidstatement and proof · cited by 39
- IsRelPrime.prod_leftproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Finset.prod_dvd_of_isRelPrimeproof · cited by 3
- IsRelPrime.pow_rightproof · cited by 1
- Finset.squarefree_prod_of_pairwise_isCoprimeproof · cited by 1
- UniqueFactorizationMonoid.radical_prodproof · cited by 0