Research proof index

SymEnv being well-formed implies that any attribute function is well-formed

The handler writes only the cells declared by demoWrites.

The append node predicate at a left-embedded index reduces to the left shape's predicate.

The append node predicate at a right-embedded index reduces to the right shape's predicate.

Successor unfolding of the sequentially-composed shape. ChallengeTreeShape.seqCompose of a family over m + 1 factors is the binary append of the head shape with the sequential composition of the tail. This is the shape-level analogue of ProtocolSpec.seqCompose_succ_eq_append, and is what lets the n-ary tree-soundness induction reduce its ste...

Chang's lemma for the large Fourier spectrum. If $f$ is nonzero and $\eta>0$, there is a subset $\Delta$ of the $\eta$-large spectrum such that the entire large spectrum lies in the additive span of $\Delta$. The theorem also gives the explicit bound $|\Delta| \le \left\lceil C e\,\left\lceil \mathcal L\!\left(\|f\|_1^2/(\|f\|_2^2|G|)\right)\right\rceil/\eta^2\right\rceil$, with the project's constant $C$.