Theorems · Theorem · group theory
Finset.dvd_prod_of_mem
∀ {ι : Type u_1} {M : Type u_3} [inst : CommMonoid M] (f : ι → M) {a : ι} {s : Finset ι}, a ∈ s → f a ∣ ∏ i ∈ s, f i- Cited by
- 23 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
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
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- dvd_mul_rightproof · cited by 89
- Finset.prod_eq_mul_prod_sdiff_singleton_of_memproof · cited by 10
Cited by23
Results whose statement or proof uses this declaration.
- ZMod.unitsMap_surjectiveproof · cited by 7
- Prime.dvd_finsetProd_iffproof · cited by 7
- Module.mem_support_iff_of_finiteproof · cited by 4
- AddMonoid.exponent_ne_zero_iff_range_addOrderOf_finiteproof · cited by 3
- Ideal.finset_inf_span_singletonproof · cited by 3
- Monoid.exponent_ne_zero_iff_range_orderOf_finiteproof · cited by 3
- Nat.dvd_of_mem_finMulAntidiagproof · cited by 3
- Field.nonempty_algHom_of_exists_rootproof · cited by 3
- Nat.Prime.dvd_primorial_iffproof · cited by 2
- Finset.lcm_dvd_prodproof · cited by 2
- Polynomial.cyclotomic.dvd_X_pow_sub_oneproof · cited by 2
- RootPairing.prod_rootFormIn_smul_coroot_mem_range_PolarizationInproof · cited by 1