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Theorems · Theorem · general algebraic systems

Finsupp.embSigma_apply_of_ne

∀ {κ : Type u_1} {ι : κ → Type u_2} {M : Type u_3} [inst : Zero M] {k k' : κ} (f : ι k →₀ M),
  k' ≠ k → ∀ (i : ι k'), f.embSigma ⟨k', i⟩ = 0

Values of embSigma f at indices outside the k-th summand are zero.

Defined in
Mathlib.Data.Finsupp.Sigma
Cited by
2 results in Mathlib
Foundations
Depth 66 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.split_embSigma_of_ne · cited by 0Finsupp.split_embSigma_of…Finsupp.embSigma_add · cited by 0Finsupp.embSigma_addDFunLike.coe · cited by 62936DFunLike.coeFinsupp · cited by 5255FinsuppFunction.Embedding.sigmaMk · cited by 25Embedding.sigmaMkFinsupp.embSigma · cited by 12Finsupp.embSigmaFinsupp.embDomain_of_notMem_range · cited by 9Finsupp.embDomain_of_notM…Finsupp.embSigma_apply_of_neCITED BYCITES

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Cited by2

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