instLinearOrderedAddCommMonoidWithTop

English

For every Archimedean S, any element x is either 0 or the top element.

Русский

Для любого Archimedean S любой элемент либо равен 0, либо верхнему элементу.

LaTeX

$$$$ \text{For all } x \in \text{ArchimedeanClass}(S): \ x = 0 \lor x = \top. $$$$

Lean4

noncomputable instance : LinearOrderedAddCommMonoidWithTop (ArchimedeanClass R) where
  top_add'
    x := by
    induction x with
    | mk x => rw [← mk_zero, ← mk_mul, zero_mul]

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