English
The length of the auxiliary sigma composition equals the blocks function value.
Русский
Длина вспомогательной сигма-композиции равна значению функции блоков.
LaTeX
$$$\\mathrm{length}(\\mathrm{Composition.sigmaCompositionAux}(a,b,i)) = \\mathrm{blocksFun}(b,i)$$$
Lean4
theorem length_gather (a : Composition n) (b : Composition a.length) : length (a.gather b) = b.length :=
show (map List.sum (a.blocks.splitWrtComposition b)).length = b.blocks.length by
rw [length_map, length_splitWrtComposition]