unitization_range — Mathlib

English

If 1 is not in s, then the unitization map is injective.

Русский

Если 1∉s, то отображение единичизации инъективно.

LaTeX

$$$\text{If } (1 \notin s) \text{ then } (unitization\ s) \text{ is injective}$$$

Lean4

theorem unitization_range : (unitization s).range = StarAlgebra.adjoin R s :=
  by
  rw [unitization, Unitization.starLift_range]
  simp only [NonUnitalStarAlgHom.coe_range, NonUnitalStarSubalgebraClass.coe_subtype, Subtype.range_coe_subtype]
  rfl

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