num_natCast — Mathlib

English

For a natural a with AtLeastTwo, the numerator of the matrix of a rational embedding equals a cast: (ofNat(a)).num = a.cast.

Русский

Принатуральном a с условием AtLeastTwo числитель матрицы равен a.cast.

LaTeX

$$$\operatorname{num}(\operatorname{ofNat}(a)) = a^{\circ}, \quad a \in \mathbb{N}, \ a \text{ satisfies } a \ge 2.$$$

Lean4

@[simp]
theorem num_natCast [DecidableEq m] (a : ℕ) : (a : Matrix m m ℚ).num = a := by
  simpa [← diagonal_natCast] using num_map_natCast (a : Matrix m m ℕ)

Похожие утверждения