Manuscript II@2 · II.tex · theorem · 50d64def

Theorem: Injective evaluation makes a fit global

Successor questions and global certification › A sufficient finite-to-global criterion · lines 1987–2003 · proof included or linked

II@2#thm:injective

Let

U = span_{R} {n_{1}, \dots, n_{L}, m} \subseteq R^{X} .

If evaluation $E_{S^{'}} : U \to R^{∣ S^{'} ∣}$ is injective and $m_{S^{'}} = N_{S^{'}} α$ , then

m = ℓ \sum α_{ℓ} n_{ℓ} on X .

Proof. The difference belongs to $U$ and has zero evaluation. Injectivity makes it the zero function.

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