Theorems · Theorem · general algebraic systems
DFinsupp.mem_support_toFun
∀ {ι : Type u} {β : ι → Type v} [inst : DecidableEq ι] [inst_1 : (i : ι) → Zero (β i)]
[inst_2 : (i : ι) → (x : β i) → Decidable (x ≠ 0)] (f : Π₀ (i : ι), β i) (i : ι), i ∈ f.support ↔ f i ≠ 0- Defined in
- Mathlib.Data.DFinsupp.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqZeroDecidable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Multisetproof · cited by 2,627
- DFinsuppstatement and proof · cited by 694
- Finset.mem_filterproof · cited by 185
- DFinsupp.supportstatement · cited by 158
- Truncproof · cited by 39
- Multiset.mem_toFinsetproof · cited by 39
- Trunc.mkproof · cited by 21
- DFinsupp.casesOnproof · cited by 6
- Trunc.induction_onproof · cited by 5
- DFinsupp.coe_mk'proof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- DFinsupp.mem_support_iffproof · cited by 13
- DFinsupp.sum_mapRange_indexproof · cited by 3
- DFinsupp.sum_add_indexproof · cited by 1
- DFinsupp.sum_of_support_subsetproof · cited by 1
- DFinsupp.sum_subtypeDomain_indexproof · cited by 0
- sigmaFinsuppEquivDFinsupp_supportproof · cited by 0