Theorems · Theorem · general algebraic systems
Finsupp.notMem_support_iff
∀ {α : Type u_1} {M : Type u_4} [inst : Zero M] {f : α →₀ M} {a : α}, a ∉ f.support ↔ f a = 0- Defined in
- Mathlib.Data.Finsupp.Defs
- Cited by
- 44 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Zero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 · cited by 13,712
- Finsuppstatement and proof · cited by 5,255
- Finsupp.supportstatement · cited by 828
- Finsupp.mem_support_iffproof · cited by 89
- not_iff_commproof · cited by 32
Cited by44
Results whose statement or proof uses this declaration.
- Finsupp.sum_of_support_subsetproof · cited by 21
- Finsupp.sum_eq_singleproof · cited by 18
- Finsupp.sum_mapRange_indexproof · cited by 18
- Finsupp.prod_of_support_subsetproof · cited by 13
- linearIndependent_iff'ₛproof · cited by 9
- Algebra.FormallyUnramified.finite_of_freeproof · cited by 7
- Ordinal.CNF.coeff_of_notMem_CNFproof · cited by 5
- Ordinal.CNF.eval_single_add'proof · cited by 5
- MvPolynomial.pderiv_monomialproof · cited by 4
- Finsupp.mapDomain_apply'proof · cited by 3
- Finsupp.eq_single_iffproof · cited by 3
- Finsupp.linearCombination_eq_fintype_linearCombination_applyproof · cited by 3