English
Finite-type version of indicator extension: equality of indicators under a finite embedding.
Русский
Конечная версия индикаторного продолжения: равенство индикаторов при конечном вложении.
LaTeX
$$$\\operatorname{AffineIndependent} k p \\Rightarrow \\forall {w_1,w_2},\\; (\\sum_{i} w_1 i = 1) \\land (\\sum_{i} w_2 i = 1) \\Rightarrow \\operatorname{Indicator}\\text{-equality}$$$
Lean4
/-- Affine equivalences preserve affine independence of families of points. -/
theorem affineIndependent_iff {p : ι → P} (e : P ≃ᵃ[k] P₂) : AffineIndependent k (e ∘ p) ↔ AffineIndependent k p :=
e.toAffineMap.affineIndependent_iff e.toEquiv.injective