nonsingular_zero — Mathlib

English

In a nontrivial base ring, the triple [1,1,0] is nonsingular for the Jacobian.

Русский

В ненулевой базе тройка [1,1,0] является неособой для Якобиана.

LaTeX

$$$ [1,1,0] \\in R^{3} \\quad \\Rightarrow \\quad W'.Nonsingular ![1,1,0] $$$

Lean4

theorem nonsingular_zero [Nontrivial R] : W'.Nonsingular ![1, 1, 0] :=
  by
  simp only [nonsingular_of_Z_eq_zero, equation_zero, true_and, fin3_def_ext, ← not_and_or]
  exact fun h => one_ne_zero <| by linear_combination (norm := ring1) h.1 - h.2.1

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