cast_lt — Mathlib

English

For all m,n in Num and α with appropriate structure, (m : α) < n iff m < n.

Русский

Для любых m,n ∈ Num и α с подходящей структурой, (m : α) < n эквивалентно m < n.

LaTeX

$$$ (m : \alpha) < n \iff m < n $$$

Lean4

@[simp, norm_cast]
theorem cast_lt [Semiring α] [PartialOrder α] [IsStrictOrderedRing α] {m n : Num} : (m : α) < n ↔ m < n := by
  rw [← cast_to_nat m, ← cast_to_nat n, Nat.cast_lt (α := α), lt_to_nat]

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