Theorems · Theorem · commutative algebra
IsCoprime.prod_right
∀ {R : Type u} {I : Type v} [inst : CommSemiring R] {x : R} {s : I → R} {t : Finset I},
(∀ i ∈ t, IsCoprime x (s i)) → IsCoprime x (∏ i ∈ t, s i)- Defined in
- Mathlib.RingTheory.Coprime.Lemmas
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- CommSemiringstatement and proof · cited by 10,911
- Finset.prodstatement · cited by 2,356
- IsCoprimestatement · cited by 321
- IsCoprime.prod_leftproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Finset.prod_dvd_of_coprimeproof · cited by 3
- Polynomial.separable_prod'proof · cited by 2
- IsCoprime.pow_rightproof · cited by 2
- Finset.exists_eq_pow_of_mul_eq_pow_of_coprimeproof · cited by 0