decode_encode (Array model: mixed-radix arrays, pull maps, and linear address maps via Bruhat f)

The following holds (Lean statement, in the scope of module Solutions.AModel):

theorem AModel.decode_encode {sh : Shape} {a : List ℕ} (h : AModel.Valid sh a) : decode sh (encode sh a) = a

Context. The lemma belongs to the part Array model: mixed-radix arrays, pull maps, and linear address maps via Bruhat factors: Arrays are lists in row-major lexicographic order over fields (first field most significant). All denotations are plain List functions.

Formalization Note. This lemma belongs to layer 5 of the Lean formalization (integer-multiplication-kappa campaign) of the OpenAI preprint Integer multiplication below $n\log n$: the uniform item-language machine (register programs over the NLogN multitape framework) assembling the Proposition 14 / Lemma 13 / Proposition 18 pieces, the resampling and chirp stages and the cost recurrences into one fixed machine, culminating in NLogN.KFTop.kappa_bound : IntMul.KappaBound (1 / 2 ^ 182) (the bound of Def_IntMul_MultitapeModel). All names refer to the definition bundles up to IntMul_Kappa_K_Defs33.