Theorems · Theorem · group theory
Finset.prod_attach
∀ {ι : Type u_1} {M : Type u_4} [inst : CommMonoid M] (s : Finset ι) (f : ι → M), ∏ x ∈ s.attach, f ↑x = ∏ x ∈ s, f x- Cited by
- 22 results in Mathlib
- Foundations
- Depth 77 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.
Cites8
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
- Function.Injective.injOnproof · cited by 280
- Subtype.coe_injectiveproof · cited by 205
- Finset.attachstatement · cited by 168
- Finset.prod_imageproof · cited by 17
- Finset.attach_image_valproof · cited by 6
Cited by22
Results whose statement or proof uses this declaration.
- Finset.prod_coe_sortproof · cited by 9
- Finset.prod_addproof · cited by 7
- MeasureTheory.Measure.eq_infinitePiproof · cited by 6
- Finset.hasProdproof · cited by 6
- MeasureTheory.Measure.infinitePi_piproof · cited by 6
- Fin.prod_univ_eq_prod_rangeproof · cited by 5
- Finset.prod_eq_prod_extendproof · cited by 3
- IsPrimitiveRoot.sub_one_norm_eq_eval_cyclotomicproof · cited by 3
- HasFDerivAt.finsetProdproof · cited by 3
- HasFDerivWithinAt.finsetProdproof · cited by 3
- Finset.prod_apply_diteproof · cited by 2
- Finset.tprod_subtypeproof · cited by 2