orderTop_eq_finiteArchimedeanClassMk

English

Equality of orderTop under an isomorphism corresponds to Archimedeanmk of the input.

Русский

Эквивалентность orderTop через изоморфизм соответствует Archimedeanmk входа.

LaTeX

$$$ orderTop\_eq\_archimedeanClassMk(f) $$$

Lean4

theorem orderTop_eq_finiteArchimedeanClassMk [IsOrderedAddMonoid R] [Archimedean R] {x : f.val.domain}
    (hx0 : x.val ≠ 0) : (ofLex (f.val x)).orderTop = FiniteArchimedeanClass.mk x.val hx0 :=
  by
  apply_fun FiniteArchimedeanClass.withTopOrderIso M
  simp [orderTop_eq_archimedeanClassMk]

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