English
There is a canonical coercion from SpecialLinearGroup to GLPos, realized as inclusion into GL and then into GLPos, compatible with the algebraic structure.
Русский
Существует каноническое приведение из SpecialLinearGroup в GLPos, реализованное как включение в GL, затем в GLPos, совместимое с структурой алгебры.
LaTeX
$$Coefficient compatibility: Coe(SpecialLinearGroup → GLPos) is the inclusion map that respects multiplication and identity.$$
Lean4
theorem sub_scalar_sq_eq_disc [NeZero (2 : K)] : (m - scalar _ (m.trace / 2)) ^ 2 = scalar _ (m.disc / 4) :=
by
simp only [scalar_apply, trace_fin_two, disc_fin_two, trace_fin_two, det_fin_two, sq, (by norm_num : (4 : K) = 2 * 2)]
ext i j
fin_cases i <;> fin_cases j <;>
· simp [Matrix.mul_apply]
field_simp
ring