English
A subspace (submodule) of a strictly convex space is itself strictly convex.
Русский
Любое подпространство strictly выпуклого пространства по сути также строго выпукло.
LaTeX
$$$[\\text{StrictConvexSpace}_{\\mathbb{K}}(E)] \\Rightarrow [\\text{StrictConvexSpace}_{\\mathbb{K}}(P)]$ для любого подпространства $P\\le E$.$$
Lean4
/-- A vector subspace of a strict convex space is a strict convex space.
This instance has priority 900
to make sure that instances like `LinearIsometry.strictConvexSpace_range`
are tried before this one. -/
instance (priority := 900) instStrictConvexSpace [StrictConvexSpace 𝕜 E] (p : Submodule 𝕜 E) : StrictConvexSpace 𝕜 p :=
p.subtypeₗᵢ.strictConvexSpace