transfiniteCompositions_iff — Mathlib

English

Characterization of transfinite compositions via iSup decomposition.

Русский

Картирование трансфинитных композиций через разложение iSup.

LaTeX

$$$transfiniteCompositions\\ f \\iff \\exists J, \\text{...}$$$

Lean4

theorem transfiniteCompositions_iff {X Y : C} (f : X ⟶ Y) :
    transfiniteCompositions.{w} W f ↔
      ∃ (J : Type w) (_ : LinearOrder J) (_ : SuccOrder J) (_ : OrderBot J) (_ : WellFoundedLT J),
        W.transfiniteCompositionsOfShape J f :=
  by simp only [transfiniteCompositions, iSup_iff]

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