Theorems · Theorem · group theory
Finset.prod_eq_single
∀ {ι : Type u_1} {M : Type u_4} [inst : CommMonoid M] {s : Finset ι} {f : ι → M} (a : ι),
(∀ b ∈ s, b ≠ a → f b = 1) → (a ∉ s → f a = 1) → ∏ x ∈ s, f x = f a- Cited by
- 7 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.prodstatement · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finset.prod_congrproof · cited by 646
- Finset.prod_const_oneproof · cited by 100
- by_casesproof · cited by 31
- Finset.prod_eq_single_of_memproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- Finset.prod_dite_eqproof · cited by 3
- Finset.prod_dite_eq'proof · cited by 3
- Fintype.prod_eq_singleproof · cited by 2
- Finsupp.prod_eq_singleproof · cited by 1
- Int.prod_modEq_singleproof · cited by 0
- Nat.multinomial_singleproof · cited by 0
- Nat.prod_modEq_singleproof · cited by 0