not_bddBelow_range_of_isPredArchimedean

English

The predecessor of a maximum equals the maximum of predecessors: pred(max(a,b)) = max(pred(a), pred(b)).

Русский

Пред predecessor для максимума равен максимуму предшествований: pred(max(a,b)) = max(pred(a), pred(b)).

LaTeX

$$$ \forall a,b,\ pred(\max(a,b)) = \max(pred(a), pred(b)).$$$

Lean4

theorem not_bddBelow_range_of_isPredArchimedean [NoMaxOrder α] [PredOrder β] [IsPredArchimedean β] (hf : StrictAnti f) :
    ¬BddBelow (Set.range f) :=
  hf.dual_right.not_bddAbove_range_of_isSuccArchimedean

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