Theorems · Theorem · commutative algebra
IsCoprime.prod_left
∀ {R : Type u} {I : Type v} [inst : CommSemiring R] {x : R} {s : I → R} {t : Finset I},
(∀ i ∈ t, IsCoprime (s i) x) → IsCoprime (∏ i ∈ t, s i) x- Defined in
- Mathlib.RingTheory.Coprime.Lemmas
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 59 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.
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
- CommSemiringstatement and proof · cited by 10,911
- Finset.prodstatement and proof · cited by 2,356
- IsCoprimestatement and proof · cited by 321
- Finset.consproof · cited by 221
- Finset.cons_inductionproof · cited by 85
- Finset.prod_consproof · cited by 60
- Finset.forall_mem_consproof · cited by 12
- isCoprime_one_leftproof · cited by 8
- IsCoprime.mul_leftproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- IsCoprime.pow_leftproof · cited by 5
- IsCoprime.prod_rightproof · cited by 4
- exists_sum_eq_one_iff_pairwise_coprimeproof · cited by 1