image_ennreal_ofReal — Mathlib

English

If s ⊆ Real is ordered-connected, then the image ENNReal.ofReal(s) is ordered-connected.

Русский

Если s ⊆ Real упордочно-связно, то образ ENNReal.ofReal(s) тоже упорядоченно-связан.

LaTeX

$$$$ (\\mathrm{ofReal} '' s).OrdConnected $$$$

Lean4

theorem image_ennreal_ofReal (h : s.OrdConnected) : (ENNReal.ofReal '' s).OrdConnected := by
  simpa only [image_image] using h.image_real_toNNReal.image_coe_nnreal_ennreal

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