ext_of_isTriangulatedClosed₂' — Mathlib

English

Under isomorphisms, the isoClosure of a triangle component remains triangulated-closed, providing a stable closure property across rotated triangles.

Русский

При изоморфизмах closure-треугольника сохраняет треангулированную замкнутость по компонентам вращения.

LaTeX

$$$\\text{isoClosure is closed under rotation: } P.isoClosure(T_1) \\Rightarrow P.isoClosure(rot\\,T_1).$$$

Lean4

theorem ext_of_isTriangulatedClosed₂' [P.IsTriangulatedClosed₂] (T : Triangle C) (hT : T ∈ distTriang C) (h₁ : P T.obj₁)
    (h₃ : P T.obj₃) : P.isoClosure T.obj₂ :=
  IsTriangulatedClosed₂.ext₂' T hT h₁ h₃

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