instPredOrderAdditive — Mathlib

English

If X is a preorder with a predecessor order, then the additive structure on X inherits the same predecessor order: PredOrder (Additive X).

Русский

Если X — предorder с predecessorial order, то Additive X сохраняет этот порядок: PredOrder (Additive X).

LaTeX

$$$$\forall X\ [\text{Preorder } X]\ [\text{PredOrder } X] \Rightarrow [\text{PredOrder } (\text{Additive } X)]$$$$

Lean4

instance [Preorder X] [h : PredOrder X] : PredOrder (Additive X) :=
  h

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