length_sigmaCompositionAux — Mathlib

English

This equality expresses a structural relation between lengths in a composed setup.

Русский

Это равенство выражает структурное соотношение длин в композиционной настройке.

LaTeX

$$$\\mathrm{length}(\\mathrm{sigmaCompositionAux}(a,b,i)) = \\mathrm{blocksFun}(b,i)$$$

Lean4

theorem length_sigmaCompositionAux (a : Composition n) (b : Composition a.length) (i : Fin b.length) :
    Composition.length (Composition.sigmaCompositionAux a b ⟨i, (length_gather a b).symm ▸ i.2⟩) =
      Composition.blocksFun b i :=
  show List.length ((splitWrtComposition a.blocks b)[i.1]) = blocksFun b i by
    rw [getElem_map_rev List.length, getElem_of_eq (map_length_splitWrtComposition _ _), blocksFun, get_eq_getElem]

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