[Merged by Bors] - feat(Geometry/Euclidean/Projection): projection onto sup#30703
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[Merged by Bors] - feat(Geometry/Euclidean/Projection): projection onto sup#30703jsm28 wants to merge 19 commits intoleanprover-community:masterfrom
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Add a lemma
```lean
lemma orthogonalProjection_eq_iff_mem {s : AffineSubspace ℝ P} [Nonempty s]
[s.direction.HasOrthogonalProjection] {p q : P} :
orthogonalProjection s p = q ↔ q ∈ s ∧ p -ᵥ q ∈ s.directionᗮ := by
```
that gives the characteristic property of the orthogonal projection in
a more convenient form to use than the existing
`inter_eq_singleton_orthogonalProjection` (from which it is derived).
Add instances that the supremum of two affine subspaces, either one nonempty, is nonempty. These are useful when working with orthogonal projections onto such a supremum.
…ion_sup_of_orthogonalProjection_eq
Add a lemma that, if the orthogonal projections of a point onto two subspaces are equal, so is the projection onto their supremum.
PR summary 4086670d5aImport changes for modified filesNo significant changes to the import graph Import changes for all files
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## more verbose report:
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Co-authored-by: Eric Wieser <[email protected]>
…sup_of_orthogonalProjection_eq
…ion_sup_of_orthogonalProjection_eq
…ion_sup_of_orthogonalProjection_eq
Co-authored-by: Eric Wieser <[email protected]>
…ion_sup_of_orthogonalProjection_eq
…sup_of_orthogonalProjection_eq
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Add a lemma that, if the orthogonal projections of a point onto two subspaces are equal, so is the projection onto their supremum.
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…community#30703) Add a lemma that, if the orthogonal projections of a point onto two subspaces are equal, so is the projection onto their supremum.
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…community#30703) Add a lemma that, if the orthogonal projections of a point onto two subspaces are equal, so is the projection onto their supremum.
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Add a lemma that, if the orthogonal projections of a point onto two subspaces are equal, so is the projection onto their supremum.