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Write $N(a_1,\dots ,a_m)$ for the limiting spreading model norm. We show that deleting any one coefficient does not increase it; iteration then gives every finite suppression.

Fix an index $r$, the coefficients, and a small $\eta >0$. Choose a generation threshold so that all the relevant full and shortened combinations beyond it approximate their model norms within $\eta$. Fix the indices before position $r$ beyond this threshold. Since $(x_n)$ is a weakly null sequence, the Mazur lemma gives a finite convex combinationwith every $j$ after the fixed prefix. Choose the remaining indices after $\max F$. For every $j\in F$, the full ordered combination with $x_j$ in slot $r$ has norm at most $N(a)+\eta$. Averaging these combinations givesThe shortened combination has norm at most $N(a)+(1+|a_r|)\eta$, and approximates its own model norm within $\eta$. Letting $\eta \downarrow 0$ provesfor every finite set $A$. Thus the model is a suppression-unconditional basic sequence with constant one. The convex-combination argument allows the omitted coordinate to sit between two retained coordinates; simply letting a single omitted index tend to infinity with all others fixed would not respect their order.