Theorems · Theorem · group theory
Finset.prod_singleton
∀ {ι : Type u_1} {M : Type u_4} [inst : CommMonoid M] (f : ι → M) (a : ι), ∏ x ∈ {a}, f x = f a- Cited by
- 78 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- mul_oneproof · cited by 3,885
- Finset.prodstatement · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finset.fold_singletonproof · cited by 2
Cited by78
Results whose statement or proof uses this declaration.
- Finsupp.prod_single_indexproof · cited by 26
- Fin.prod_univ_twoproof · cited by 16
- Matrix.det_uniqueproof · cited by 15
- Polynomial.cyclotomic_primeproof · cited by 7
- Multipliable.tendsto_cofinite_oneproof · cited by 6
- Finset.prod_eq_single_of_memproof · cited by 5
- Nat.uniformBell_eqproof · cited by 5
- ProbabilityTheory.setBernoulli_ae_subsetproof · cited by 5
- tprod_eq_mulSingleproof · cited by 5
- Finset.prod_pairproof · cited by 5
- Matrix.mul_adjp_apply_eqproof · cited by 4
- MvPolynomial.uniqueAlgEquiv_monomialproof · cited by 4