ofUpperSet_inj — Mathlib

English

The map ofUpperSet is injective on upper-set objects: toUpperSet(a) = toUpperSet(b) implies a = b for a,b in WithUpperSet α.

Русский

Отображение ofUpperSet инъективно на элементах WithUpperSet α: если toUpperSet(a) = toUpperSet(b), то a = b.

LaTeX

$$$\forall {a,b:\mathrm{WithUpperSet}(\alpha)}\; \mathrm{ofUpperSet}(a) = \mathrm{ofUpperSet}(b) \Rightarrow a=b$$$

Lean4

theorem ofUpperSet_inj {a b : WithUpperSet α} : ofUpperSet a = ofUpperSet b ↔ a = b :=
  Iff.rfl

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