Theorems · Theorem · general algebraic systems
Finsupp.embDomain_of_notMem_range
∀ {α : Type u_1} {β : Type u_2} {M : Type u_4} [inst : Zero M] (f : α ↪ β) (v : α →₀ M),
∀ a ∉ Set.range ⇑f, (Finsupp.embDomain f v) a = 0- Defined in
- Mathlib.Data.Finsupp.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 65 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 and proof · cited by 62,936
- Setstatement · cited by 53,352
- Finsuppstatement and proof · cited by 5,255
- Set.rangestatement and proof · cited by 4,705
- Function.Embeddingstatement and proof · cited by 988
- Finsupp.embDomainstatement · cited by 69
Cited by9
Results whose statement or proof uses this declaration.
- Finsupp.embDomain_eq_mapDomainproof · cited by 13
- Finsupp.embDomain_some_noneproof · cited by 2
- Finsupp.embSigma_apply_of_neproof · cited by 2
- List.toFinsupp_appendproof · cited by 2
- Finsupp.embDomain_comapDomainproof · cited by 2
- LinearMap.singularValues_of_finrank_leproof · cited by 1
- Finsupp.embDomain_notin_rangeproof · cited by 0
- Finsupp.extendDomain_eq_embDomain_subtypeproof · cited by 0
- Finsupp.embSigma_applyproof · cited by 0