Theorems · Theorem · group theory
Submonoid.coe_finsetProd
∀ {ι : Type u_4} {M : Type u_5} [inst : CommMonoid M] (S : Submonoid M) (f : ι → ↥S) (s : Finset ι),
↑(∏ i ∈ s, f i) = ∏ i ∈ s, ↑(f i)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Submonoidstatement and proof · cited by 3,086
- Finset.prodstatement · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- map_prodproof · cited by 108
- Submonoid.subtypeproof · cited by 26
Cited by4
Results whose statement or proof uses this declaration.
- IsLocalization.exist_integer_multiplesproof · cited by 4
- IsLocalizedModule.exist_integer_multiplesproof · cited by 3
- Submodule.annihilator_top_inter_nonZeroDivisorsproof · cited by 1
- Submonoid.coe_finset_prodproof · cited by 0