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Theorems · Theorem · group theory

Finset.prod_eq_ite

∀ {ι : Type u_1} {M : Type u_4} [inst : CommMonoid M] [inst_1 : DecidableEq ι] {s : Finset ι} {f : ι → M} (a : ι),
  (∀ b ∈ s, b ≠ a → f b = 1) → ∏ x ∈ s, f x = if a ∈ s then f a else 1
Defined in
Mathlib.Algebra.BigOperators.Group.Finset.Basic
Cited by
2 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidDecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Int.prod_modEq_ite · cited by 0Int.prod_modEq_iteNat.prod_modEq_ite · cited by 0Nat.prod_modEq_iteFinset · cited by 13712FinsetFinset.prod · cited by 2356Finset.prodCommMonoid · cited by 2264CommMonoidFinset.prod_congr · cited by 646Finset.prod_congrFinset.prod_const_one · cited by 100Finset.prod_const_oneFinset.prod_eq_single_of_mem · cited by 5Finset.prod_eq_single_of_…Finset.prod_eq_iteCITED BYCITES

Cites6

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Cited by2

Results whose statement or proof uses this declaration.