Theorems · Theorem · ring theory
Finsupp.prod_of_support_subset
∀ {α : Type u_1} {M : Type u_8} {N : Type u_10} [inst : Zero M] [inst_1 : CommMonoid N] (f : α →₀ M) {s : Finset α},
f.support ⊆ s → ∀ (g : α → M → N), (∀ i ∈ s, g i 0 = 1) → f.prod g = ∏ x ∈ s, g x (f x)- Cited by
- 13 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ZeroCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- Finsuppstatement and proof · cited by 5,255
- Finset.prodstatement · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finsupp.supportstatement and proof · cited by 828
- Finsupp.prodstatement · cited by 231
- Finsupp.notMem_support_iffproof · cited by 44
- Finset.prod_subsetproof · cited by 31
Cited by13
Results whose statement or proof uses this declaration.
- Finsupp.prod_single_indexproof · cited by 26
- Finsupp.prod_add_indexproof · cited by 6
- Finsupp.prod_fintypeproof · cited by 4
- MvPolynomial.expand_monomialproof · cited by 3
- MvPowerSeries.monomial_smul_eqproof · cited by 2
- ArithmeticFunction.IsMultiplicative.lcm_apply_mul_gcd_applyproof · cited by 2
- Finsupp.prod_indicator_index_eq_prod_attachproof · cited by 1
- MvPowerSeries.expand_monomialproof · cited by 1
- Nat.factorizationLCMLeft_dvd_leftproof · cited by 1
- Finsupp.prod_congr_of_eq_on_unionproof · cited by 1
- Nat.factorizationLCMRight_dvd_rightproof · cited by 1
- Finsupp.multinomial_of_support_subsetproof · cited by 0