isComplete_image_iff' — Mathlib

English

Same as the previous result, with a streamlined variant for complete-image under semilinear isometries.

Русский

То же самое в упрощённой форме для изображений полноты под полулинейкими изометриями.

LaTeX

$$IsComplete (f''S) \iff IsComplete(S)$$

Lean4

@[simp]
  -- Should be replaced with `LinearIsometry.isComplete_image_iff` when https://github.com/leanprover/lean4/issues/3107 is fixed.

theorem isComplete_image_iff' (f : LinearIsometry σ₁₂ E E₂) {s : Set E} : IsComplete (f '' s) ↔ IsComplete s :=
  LinearIsometry.isComplete_image_iff _

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