Theorems · Theorem · group theory

Fintype.prod_of_injective

∀ {M : Type u_4} {κ : Type u_6} {ι : Type u_7} [inst : Fintype ι] [inst_1 : Fintype κ] [inst_2 : CommMonoid M]
  (e : ι → κ),
  Function.Injective e →
    ∀ (f : ι → M) (g : κ → M), (∀ i ∉ Set.range e, g i = 1) → (∀ (i : ι), f i = g (e i)) → ∏ i, f i = ∏ j, g j

Defined in: Mathlib.Algebra.BigOperators.Group.Finset.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype Fintype CommMonoid

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

Setstatement · cited by 53,352
Fintypestatement and proof · cited by 7,736
Set.imageproof · cited by 5,609
Set.rangestatement and proof · cited by 4,705
Set.univproof · cited by 3,945
Finset.univstatement and proof · cited by 3,473
Finset.prodstatement · cited by 2,356
CommMonoidstatement and proof · cited by 2,264
Set.MapsToproof · cited by 732
Set.image_univproof · cited by 322
Function.Injective.injOnproof · cited by 280
Finset.coe_univproof · cited by 101

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