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Theorems · Theorem · ring theory

Finsupp.prod_single_index

∀ {α : Type u_1} {M : Type u_8} {N : Type u_10} [inst : Zero M] [inst_1 : CommMonoid N] {a : α} {b : M} {h : α → M → N},
  h a 0 = 1 → (fun₀ | a => b).prod h = h a b
Defined in
Mathlib.Algebra.BigOperators.Finsupp.Basic
Cited by
26 results in Mathlib
Foundations
Depth 69 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.

MvPolynomial.eval₂_X · cited by 36MvPolynomial.eval₂_XMvPolynomial.eval₂_mul · cited by 21MvPolynomial.eval₂_mulwittPolynomial_eq_sum_C_mul_X_pow · cited by 8wittPolynomial_eq_sum_C_m…MvPolynomial.eval₂_uniqueAlgEquiv · cited by 4MvPolynomial.eval₂_unique…PowerSeries.coeff_subst · cited by 4PowerSeries.coeff_substNat.multiplicative_factorization · cited by 3Nat.multiplicative_factor…PowerSeries.rescale_eq · cited by 3PowerSeries.rescale_eqaeval_wittPolynomial · cited by 3aeval_wittPolynomialMvPolynomial.coeff_X_pow · cited by 2MvPolynomial.coeff_X_powMvPolynomial.eval₂_mul_monomial · cited by 2MvPolynomial.eval₂_mul_mo…Subgroup.exists_finsupp_of_mem_closure_range · cited by 2Subgroup.exists_finsupp_o…Submonoid.exists_finsupp_of_mem_closure_range · cited by 2Submonoid.exists_finsupp_…Matrix.toMvPolynomial_mul · cited by 1Matrix.toMvPolynomial_mulFinsupp.image_pow_eq_finsuppProd_image · cited by 1Finsupp.image_pow_eq_fins…FormalGroup.coeff_one_Xzero · cited by 1FormalGroup.coeff_one_Xze…DFunLike.coe · cited by 62936DFunLike.coeCommMonoid · cited by 2264CommMonoidFinsupp.single · cited by 943Finsupp.singleFinsupp.prod · cited by 231Finsupp.prodFinsupp.single_eq_same · cited by 171Finsupp.single_eq_sameFinset.mem_singleton · cited by 103Finset.mem_singletonFinset.prod_singleton · cited by 78Finset.prod_singletonFinsupp.support_single_subset · cited by 27Finsupp.support_single_su…Finsupp.prod_of_support_subset · cited by 13Finsupp.prod_of_support_s…Finsupp.prod_single_indexCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by26

Results whose statement or proof uses this declaration.