proj_comp_single_of_same — Mathlib

English

If the pi Q is anisotropic, then each Q_i is anisotropic.

Русский

Если pi Q анизотропна, то каждая компонента Q_i анизотропна.

LaTeX

$$$ (\\pi Q).\\mathrm{Anisotropic} \\Rightarrow \\forall i, Q_i.\\mathrm{Anisotropic}. $$$

Lean4

/-- Note that `QuadraticMap.Isometry.id` would not be well-typed as the RHS. -/
@[simp]
theorem proj_comp_single_of_same [Fintype ι] [DecidableEq ι] (i : ι) (Q : QuadraticMap R (Mᵢ i) P) :
    (proj i Q).comp (single _ i) = .ofEq (Pi.single_eq_same _ _) :=
  ext fun _ => Pi.single_eq_same _ _

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