succ_natCast — Mathlib

English

If X is a preorder with PredOrder and IsPredArchimedean X, then Multiplicative X is IsPredArchimedean.

Русский

Если X — предorder с PredOrder и IsPredArchimedean X, то Multiplicative X сохраняет это свойство.

LaTeX

$$$$\forall X\ [\text{Preorder } X] [\text{PredOrder } X] [\text{IsPredArchimedean } X],\ \ \ IsPredArchimedean (\text{Multiplicative } X)$$$$

Lean4

theorem succ_natCast (n : ℕ) : succ (n : WithBot α) = n + 1 := by
  rw [← WithBot.coe_natCast, succ_coe, Order.succ_eq_add_one]

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