length_transposeL (KFY 10: `tensorGo` as an iteration over rotated shapes)

The following holds (Lean statement, in the scope of module Solutions.KFY10Iter):

theorem NLogN.KFY.length_transposeL (n m : ℕ) (L : List GI) : (transposeL n m L).length = m * n

Context. The lemma belongs to the part KFY 10: tensorGo as an iteration over rotated shapes: stepL R f L: transpose the head axis of the shape R to the end (transposeL), apply f to the consecutive lines. iterL dims fs k applies the steps for the rotations dims.rotate j, j < k. tensorGo_iterL: tensorGo of the list (dims_i, fs i)_i is iterL dims fs d.

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.