Theorems · Theorem · group theory

Set.mem_prod_list_ofFn

∀ {α : Type u_1} [inst : Monoid α] {n : ℕ} {a : α} {s : Fin n → Set α},
  a ∈ (List.ofFn s).prod ↔ ∃ f, (List.ofFn fun i => ↑(f i)).prod = a

Defined in: Mathlib.Algebra.Group.Pointwise.Set.ListOfFn
Cited by: 2 results in Mathlib
Foundations: Depth 47 from the axioms · uses propext, Quot.sound
Assumes: Monoid

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Cites8

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

Setstatement and proof · cited by 53,352
Set.Elemstatement and proof · cited by 7,166
Monoidstatement and proof · cited by 3,887
Set.mulstatement · cited by 297
Fin.consproof · cited by 190
Fin.cons_succproof · cited by 54
Set.onestatement · cited by 54
Fin.cons_zeroproof · cited by 53

Cited by2

Results whose statement or proof uses this declaration.

Set.mem_powproof · cited by 3
Finset.mem_prod_list_ofFnproof · cited by 0