Research proof index

For ℓ = 1, coordinate-wise special soundness is ordinary k-special soundness: the challenge values are distinct, and there is a central vector together with k - 1 siblings differing in the single coordinate , i.e. k pairwise-distinct challenge values.

For a single coordinate (ℓ = 1), membership in the special-sound family SS(S, 1, k) is exactly injectivity of the k challenge vectors: a central vector together with k-1 siblings differing in the unique coordinate is just k pairwise-distinct values. This is the cleaner ℓ = 1 characterization underlying the bridge to plain k-special soundness.

Any Process can be obtained by filling a Context with an atom. This proves that Context is a complete formalisation of syntactic contexts for CCS.

Arbitrary intersections of facts are facts.

Theory equivalence is a bisimulation.

Remove unnecessary hypotheses. This can't be computable because it requires picking an order on the finset Δ.