instNonemptyOctahedron — Mathlib

English

The triple-rotation isomorphism is established with the triangle structure; this is a component of the triple rotation identity.

Русский

Изоморфизм тройного поворота в структуре треугольника установлен; это компонент тождественного свойства тройного поворота.

LaTeX

$$$\\text{rotateRotateRotateIso}(C) : (\\text{rotate } C)^{\\circ 3} \\cong \\text{Triangle.shiftFunctor} C 1$$$

Lean4

instance (X : C) :
    Nonempty
      (Octahedron (comp_id (𝟙 X)) (contractible_distinguished X) (contractible_distinguished X)
        (contractible_distinguished X)) :=
  by
  refine
    ⟨⟨0, 0, ?_, ?_, ?_, ?_,
        isomorphic_distinguished _ (contractible_distinguished (0 : C)) _
          (Triangle.isoMk _ _ (by rfl) (by rfl) (by rfl))⟩⟩
  all_goals apply Subsingleton.elim

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