Theorems · Theorem · ring theory
Finsupp.sum_congr
∀ {α : Type u_1} {M : Type u_8} {N : Type u_10} [inst : Zero M] [inst_1 : AddCommMonoid N] {f : α →₀ M}
{g1 g2 : α → M → N}, (∀ x ∈ f.support, g1 x (f x) = g2 x (f x)) → f.sum g1 = f.sum g2- Cited by
- 14 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ZeroAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Finsetstatement · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finsuppstatement and proof · cited by 5,255
- Finset.sum_congrproof · cited by 2,323
- Finsupp.supportstatement and proof · cited by 828
- Finsupp.sumstatement · cited by 481
Cited by14
Results whose statement or proof uses this declaration.
- Finsupp.sum_mapDomain_indexproof · cited by 19
- Finsupp.mapDomain_compproof · cited by 13
- MonoidAlgebra.coeff_single_mul_eq_mul_coeffproof · cited by 4
- MonoidAlgebra.coeff_mul_single_eq_coeff_mulproof · cited by 4
- AddMonoidAlgebra.coeff_mul_single_eq_coeff_mulproof · cited by 3
- AddMonoidAlgebra.coeff_single_mul_eq_mul_coeffproof · cited by 3
- Ideal.range_finsuppTotalproof · cited by 1
- Submodule.inf_iSup_genEigenspaceproof · cited by 1
- MonoidAlgebra.coeff_mul_apply_leftproof · cited by 1
- MonoidAlgebra.coeff_mul_apply_rightproof · cited by 1
- LinearMap.commute_transvections_iff_of_basisproof · cited by 0
- AddMonoidAlgebra.coeff_mul_apply_leftproof · cited by 0