Theorems · Theorem · commutative algebra
IsCoprime.prod_left_iff
∀ {R : Type u} {I : Type v} [inst : CommSemiring R] {x : R} {s : I → R} {t : Finset I},
IsCoprime (∏ i ∈ t, s i) x ↔ ∀ i ∈ t, IsCoprime (s i) x- Defined in
- Mathlib.RingTheory.Coprime.Lemmas
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 61 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.
Cites9
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.induction_onproof · cited by 167
- Finset.prod_insertproof · cited by 109
- Finset.forall_mem_insertproof · cited by 19
- isCoprime_one_leftproof · cited by 8
- IsCoprime.mul_left_iffproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- IsCoprime.prod_right_iffproof · cited by 2
- IsCoprime.of_prod_leftproof · cited by 1