transfiniteCompositions_monotone — Mathlib

English

The map W ↦ transfiniteCompositions is monotone with respect to W.

Русский

Карта W ↦ трансфинитные композиции монотонна по W.

LaTeX

$$Monotone(transfiniteCompositions)$$

Lean4

theorem transfiniteCompositions_monotone : Monotone (transfiniteCompositions.{w} (C := C)) :=
  by
  intro W₁ W₂ h X Y f hf
  rw [transfiniteCompositions_iff] at hf
  obtain ⟨J, _, _, _, _, hf⟩ := hf
  exact
    transfiniteCompositionsOfShape_le_transfiniteCompositions _ _ _ (transfiniteCompositionsOfShape_monotone J h _ hf)

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