Theorems · Theorem · group theory
Finset.prod_eq_one
∀ {ι : Type u_1} {M : Type u_4} {s : Finset ι} [inst : CommMonoid M] {f : ι → M}, (∀ x ∈ s, f x = 1) → ∏ x ∈ s, f x = 1- Cited by
- 22 results in Mathlib
- Foundations
- Depth 56 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.
Cites5
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
Cited by22
Results whose statement or proof uses this declaration.
- MeasureTheory.measurePreserving_evalproof · cited by 5
- Finset.prod_subset_one_on_sdiffproof · cited by 4
- Finset.prod_mulIndicator_eq_prod_filterproof · cited by 4
- Lagrange.eval_basis_selfproof · cited by 3
- Finset.prod_dite_eqproof · cited by 3
- Finset.prod_dite_eq'proof · cited by 3
- char_dvd_card_solutions_of_sum_ltproof · cited by 2
- Fintype.prod_eq_oneproof · cited by 2
- Finset.mulSupport_prodproof · cited by 1
- Complex.ECanonicalDecomp.eq_smul_meromorphicTrailingCoeffAtproof · cited by 1
- Finset.exists_ne_one_of_prod_ne_oneproof · cited by 1
- Finset.prod_ite_oneproof · cited by 1