Theorems · Theorem · group theory

Finset.prod_of_injOn

∀ {ι : Type u_1} {κ : Type u_2} {M : Type u_4} [inst : CommMonoid M] {s : Finset ι} {t : Finset κ} {f : ι → M}
  {g : κ → M} (e : ι → κ),
  Set.InjOn e ↑s →
    Set.MapsTo e ↑s ↑t → (∀ i ∈ t, i ∉ e '' ↑s → g i = 1) → (∀ i ∈ s, f i = g (e i)) → ∏ i ∈ s, f i = ∏ j ∈ t, g j

Defined in

Mathlib.Algebra.BigOperators.Group.Finset.Basic

Cited by

1 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoid