Research proof index

The per-variable / prismalinear degree-survival lemma: if a polynomial respects a per-variable degree bound b : Fin ℓ → ℕ, then fixing the first v variables to scalars produces a polynomial whose surviving Fin (ℓ-v) variables respect b restricted to their original suffix indices. Needed for SWIRL-style sumchecks where the multiplier has degree `|D...

Renaming by an equivalence e : σ ≃ τ transports a per-variable degree bound b to the pulled-back bound b ∘ e.symm on the target.

Currying via sumAlgEquiv preserves the per-variable bound on the outer (S₁) coordinates restricted to Sum.inl.

If f is negligible, then fun n => ↑(p.eval n) * f n is negligible for any polynomial p. This is the key lemma for handling polynomial-loss security reductions.

ℝ≥0∞ form of tvDist_bind_left_le_const, matching the quantitative APIs: a per-a bound ENNReal.ofReal (tvDist (f a) (g a)) ≤ ε on the support of mx lifts through the shared bind.

Support-aware bind congruence: if two continuations agree on all elements in the support of mx, the resulting bind computations are equal.