Theorems · Theorem · combinatorics
Finset.mem_finsupp_iff_of_support_subset
∀ {ι : Type u_1} {α : Type u_2} [inst : Zero α] {s : Finset ι} {f : ι →₀ α} {t : ι →₀ Finset α},
t.support ⊆ s → (f ∈ s.finsupp ⇑t ↔ ∀ (i : ι), f i ∈ t i)When t is supported on s, f ∈ s.finsupp t precisely means that f is pointwise in t.
- Defined in
- Mathlib.Data.Finset.Finsupp
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 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.
Cites11
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 and proof · cited by 13,712
- Finsuppstatement and proof · cited by 5,255
- Finsupp.supportstatement and proof · cited by 828
- Finsupp.mem_support_iffproof · cited by 89
- Finset.zerostatement · cited by 74
- Finsupp.notMem_support_iffproof · cited by 44
- Finset.mem_zeroproof · cited by 4
- Finset.finsuppstatement · cited by 4
- Finset.zero_mem_zeroproof · cited by 3
- Finset.mem_finsupp_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Finsupp.mem_piproof · cited by 0