Mathlib Map

Theorems · Theorem · general algebraic systems

Finsupp.embDomain_apply_self

∀ {α : Type u_1} {β : Type u_2} {M : Type u_4} [inst : Zero M] (f : α ↪ β) (v : α →₀ M) (a : α),
  (Finsupp.embDomain f v) (f a) = v a
Defined in
Mathlib.Data.Finsupp.Defs
Cited by
15 results in Mathlib
Foundations
Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Zero
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Finsupp.embDomain_eq_mapDomain · cited by 13Finsupp.embDomain_eq_mapD…Polynomial.coeff_reflect · cited by 9Polynomial.coeff_reflectFinsupp.sum_embDomain · cited by 6Finsupp.sum_embDomainLinearMap.singularValues_fin · cited by 4LinearMap.singularValues_…Finsupp.embDomain_injective · cited by 3Finsupp.embDomain_injecti…Finsupp.embSigma_apply_self · cited by 3Finsupp.embSigma_apply_se…Finsupp.some_embDomain_some · cited by 2Finsupp.some_embDomain_so…List.toFinsupp_append · cited by 2List.toFinsupp_appendFinsupp.comapDomain_embDomain · cited by 2Finsupp.comapDomain_embDo…Finsupp.embDomain_comapDomain · cited by 2Finsupp.embDomain_comapDo…Finsupp.prod_embDomain · cited by 1Finsupp.prod_embDomainFinsupp.single_of_embDomain_single · cited by 1Finsupp.single_of_embDoma…Finsupp.embDomain_some_some · cited by 1Finsupp.embDomain_some_so…Finsupp.extendDomain_eq_embDomain_subtype · cited by 0Finsupp.extendDomain_eq_e…Finsupp.embSigma_apply · cited by 0Finsupp.embSigma_applyDFunLike.coe · cited by 62936DFunLike.coeFinsupp · cited by 5255FinsuppFunction.Embedding · cited by 988Function.EmbeddingFinsupp.embDomain · cited by 69Finsupp.embDomainFinsupp.embDomain_apply_selfCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by15

Results whose statement or proof uses this declaration.