Theorems · Theorem · group theory
Finset.prod_map
∀ {ι : Type u_1} {κ : Type u_2} {M : Type u_3} [inst : CommMonoid M] (s : Finset ι) (e : ι ↪ κ) (f : κ → M),
∏ x ∈ Finset.map e s, f x = ∏ x ∈ s, f (e x)- Cited by
- 75 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- Multisetproof · cited by 2,627
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Function.Embeddingstatement and proof · cited by 988
- Multiset.mapproof · cited by 876
- Finset.mapstatement and proof · cited by 747
- Multiset.prodproof · cited by 528
- Finset.valproof · cited by 438
- Multiset.map_mapproof · cited by 151
- Finset.map_valproof · cited by 7
Cited by75
Results whose statement or proof uses this declaration.
- finprod_eq_prod_of_mulSupport_subsetproof · cited by 21
- Finset.prod_sigmaproof · cited by 10
- Fin.prod_univ_succAboveproof · cited by 9
- Finset.prod_addproof · cited by 7
- Finset.hasProdproof · cited by 6
- Finset.prod_disjSumproof · cited by 6
- Finset.prod_insertNoneproof · cited by 4
- Nat.Partition.hasProd_genFunproof · cited by 4
- Finset.prod_erase_attachproof · cited by 3
- Int.radical_natAbs_eq_radicalproof · cited by 3
- Units.mk0_prodproof · cited by 2
- Finset.prod_Ico_add'proof · cited by 2