range — Mathlib

English

If G is generated by x, then for any equivalence e, G is generated by x composed with e.

Русский

Если G порожден через x, то для любой эквивалентности e G порожден через x ∘ e.

LaTeX

$$$G\text{ IsGeneratedBy } x \Rightarrow \forall {ι'}\ (e:\iota' \simeq \iota),\ G\text{ IsGeneratedBy }(\lambda i'\mapsto x(e(i'))) $$$

Lean4

theorem range : (Subpresheaf.range f).IsGeneratedBy (fun i ↦ f.app _ (x i)) := by
  simpa only [← Subpresheaf.image_top] using h.image f

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