Theorems · Theorem · commutative algebra
IsRelPrime.prod_left_iff
∀ {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
- 2 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finset.induction_onproof · cited by 167
- IsRelPrimestatement and proof · cited by 136
- Finset.prod_insertproof · cited by 109
- DecompositionMonoidstatement and proof · cited by 39
- Finset.forall_mem_insertproof · cited by 19
- isRelPrime_one_leftproof · cited by 3
- IsRelPrime.mul_left_iffproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsRelPrime.prod_right_iffproof · cited by 2
- IsRelPrime.of_prod_leftproof · cited by 1