succOrder — Mathlib

English

A locally finite order becomes a PredOrder when equipped with the pred operation derived from succ.

Русский

Локально конечный порядок становится PredOrder при наличии операции предшественника, полученной из succ.

LaTeX

$$$\\text{predOrder}(\\iota) := \\text{PredOrder}$ на основe succOrder и LocallyFiniteOrder$$

Lean4

/-- A locally finite order is a `SuccOrder`.
This is not an instance, because its `succ` field conflicts with computable `SuccOrder` structures
on `ℕ` and `ℤ`. -/
noncomputable def succOrder [LocallyFiniteOrder ι] : SuccOrder ι
    where
  succ := succFn
  le_succ := le_succFn
  max_of_succ_le h := isMax_of_succFn_le _ h
  succ_le_of_lt h := succFn_le_of_lt _ _ h

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