isColimitLocallyConstantPresheafDiagram_desc_apply

English

The relation that a run of a TM2 step preserves the supports relation is equivalent to the original transition relation.

Русский

Связь того, что выполнение шага сохраняет отношение поддержки, эквивалентна исходному переходу.

LaTeX

$$$\\forall S\\; {k}\\; (s : StAct)\\; (q : TM2.Stmt),\n\\; TM2.SupportsStmt S (stRun s q) \\leftrightarrow TM2.SupportsStmt S q$$$

Lean4

@[simp]
theorem isColimitLocallyConstantPresheafDiagram_desc_apply (S : LightProfinite)
    (s : Cocone (S.diagram.rightOp ⋙ locallyConstantPresheaf X)) (n : ℕ) (f : LocallyConstant (S.diagram.obj ⟨n⟩) X) :
    (isColimitLocallyConstantPresheafDiagram X S).desc s (f.comap (S.asLimitCone.π.app ⟨n⟩).hom) = s.ι.app n f :=
  by
  change
    ((((locallyConstantPresheaf X).mapCocone (coconeRightOpOfCone S.asLimitCone)).ι.app n) ≫
          (isColimitLocallyConstantPresheafDiagram X S).desc s)
        _ =
      _
  rw [(isColimitLocallyConstantPresheafDiagram X S).fac]

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