bddAbove_range_comp — Mathlib

English

The brange of bfamilyOfFamily' equals the range of f, when maturing via type r.

Русский

brange bfamilyOfFamily' совпадает с диапазоном f, через тип r.

LaTeX

$$$\mathrm{brange}_{\text{type } r}(\mathrm{bfamilyOfFamily'}(r,f)) = \mathrm{range}(f)$$$

Lean4

theorem bddAbove_range_comp {ι : Type u} {f : ι → Ordinal.{v}} (hf : BddAbove (range f))
    (g : Ordinal.{v} → Ordinal.{max v w}) : BddAbove (range (g ∘ f)) :=
  by
  rw [range_comp]
  exact bddAbove_image hf g

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