English
Isometry preserves the perpBisector structure under preimage.
Русский
Изометрия сохраняет структуру perpBisector через предобраз.
LaTeX
$$Isometry preimage preserves perpBisector$$
Lean4
/-- The orthogonal projection of a point onto a nonempty affine
subspace, whose direction is complete, as an unbundled function. This
definition is only intended for use in setting up the bundled version
`orthogonalProjection` and should not be used once that is
defined. -/
def orthogonalProjectionFn (s : AffineSubspace ℝ P) [Nonempty s] [s.direction.HasOrthogonalProjection] (p : P) : P :=
Classical.choose <|
inter_eq_singleton_of_nonempty_of_isCompl (nonempty_subtype.mp ‹_›) (mk'_nonempty p s.directionᗮ)
(by
rw [direction_mk' p s.directionᗮ]
exact Submodule.isCompl_orthogonal_of_hasOrthogonalProjection)
