Theorems · Theorem · group theory
Finset.prod_eq_single_of_mem
∀ {ι : Type u_1} {M : Type u_4} [inst : CommMonoid M] {s : Finset ι} {f : ι → M},
∀ a ∈ s, (∀ b ∈ s, b ≠ a → f b = 1) → ∏ x ∈ s, f x = f a- Cited by
- 5 results in Mathlib
- Foundations
- Depth 68 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.
Cites6
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.mem_singletonproof · cited by 103
- Finset.prod_singletonproof · cited by 78
- Finset.prod_subsetproof · cited by 31
Cited by5
Results whose statement or proof uses this declaration.
- Finset.prod_eq_singleproof · cited by 7
- Finset.prod_eq_iteproof · cited by 2
- Finset.le_prod_max_oneproof · cited by 2
- Finset.prod_eq_mulproof · cited by 1
- Finset.prod_ite_oneproof · cited by 1