Theorems · Theorem · group theory

Finset.prod_preimage

∀ {ι : Type u_1} {κ : Type u_2} {β : Type u_3} [inst : CommMonoid β] (f : ι → κ) (s : Finset κ)
  (hf : Set.InjOn f (f ⁻¹' ↑s)) (g : κ → β),
  (∀ x ∈ s, x ∉ Set.range f → g x = 1) → ∏ x ∈ s.preimage f hf, g (f x) = ∏ x ∈ s, g x

Defined in: Mathlib.Algebra.BigOperators.Group.Finset.Preimage
Cited by: 4 results in Mathlib
Foundations: Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommMonoid

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Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
Finsetstatement and proof · cited by 13,712
SetLike.coestatement and proof · cited by 8,199
Set.preimagestatement and proof · cited by 4,946
Set.rangestatement and proof · cited by 4,705
Finset.prodstatement and proof · cited by 2,356
CommMonoidstatement and proof · cited by 2,264
Set.InjOnstatement and proof · cited by 543
Finset.preimagestatement · cited by 108
Not.imp_symmproof · cited by 25
Finset.prod_filter_of_neproof · cited by 3
Finset.prod_preimage'proof · cited by 1

Cited by4

Results whose statement or proof uses this declaration.

Function.Injective.hasProd_comap_iffproof · cited by 2
Function.Injective.map_atTop_finsetProd_eqproof · cited by 1
Finset.prod_preimage_of_bijproof · cited by 0
Function.Injective.hasProd_comap_iff_of_hasSupportproof · cited by 0