Theorems · Theorem · general algebraic systems
Finsupp.support_eq_singleton
∀ {α : Type u_1} {M : Type u_5} [inst : Zero M] {f : α →₀ M} {a : α}, f.support = {a} ↔ f a ≠ 0 ∧ f = fun₀ | a => f a- Defined in
- Mathlib.Data.Finsupp.Single
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 64 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.
Cites10
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
- Finsuppstatement and proof · cited by 5,255
- Finsupp.singlestatement and proof · cited by 943
- Finsupp.supportstatement and proof · cited by 828
- Finsupp.mem_support_iffproof · cited by 89
- Finset.mem_singleton_selfproof · cited by 44
- Finsupp.support_singleproof · cited by 39
- subset_of_eqproof · cited by 3
- Finsupp.eq_single_iffproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- WittVector.mul_polyOfInterest_aux1proof · cited by 1
- Finsupp.support_eq_singleton'proof · cited by 1