det_fderivPolarCoordSymm — Mathlib

English

The map x ↦ (descPochhammer 𝕜 n).eval x is continuous.

Русский

Картa x ↦ (descPochhammer 𝕜 n).eval x непрерывна.

LaTeX

$$$$ \text{Continuous}\left( x \mapsto \mathrm{Polynomial.eval}(x, \mathrm{descPochhammer}(\mathbb{K}, n)) \right). $$$$

Lean4

theorem det_fderivPolarCoordSymm (p : ℝ × ℝ) : (fderivPolarCoordSymm p).det = p.1 :=
  by
  conv_rhs => rw [← one_mul p.1, ← cos_sq_add_sin_sq p.2]
  unfold fderivPolarCoordSymm
  simp only [neg_mul, LinearMap.det_toContinuousLinearMap, LinearMap.det_toLin, Matrix.det_fin_two_of, sub_neg_eq_add]
  ring

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