[Merged by Bors] - feat(Geometry/Euclidean/Projection): orthogonalProjection_orthogonalProjection_of_le#30474
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…Projection_of_le` Add a lemma that `orthogonalProjection s₁ (orthogonalProjection s₂ p) = orthogonalProjection s₁ p` for `s₁ ≤ s₂`. (A similar lemma for projection onto submodules rather than affine subspaces already exists.)
PR summary 4086670d5aImport changes for modified filesNo significant changes to the import graph Import changes for all files
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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).
…ion_orthogonalProjection_of_le
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Co-authored-by: Eric Wieser <[email protected]>
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…Projection_of_le` (#30474) Add a lemma that `orthogonalProjection s₁ (orthogonalProjection s₂ p) = orthogonalProjection s₁ p` for `s₁ ≤ s₂`. (A similar lemma for projection onto submodules rather than affine subspaces already exists.)
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…Projection_of_le` (leanprover-community#30474) Add a lemma that `orthogonalProjection s₁ (orthogonalProjection s₂ p) = orthogonalProjection s₁ p` for `s₁ ≤ s₂`. (A similar lemma for projection onto submodules rather than affine subspaces already exists.)
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…Projection_of_le` (leanprover-community#30474) Add a lemma that `orthogonalProjection s₁ (orthogonalProjection s₂ p) = orthogonalProjection s₁ p` for `s₁ ≤ s₂`. (A similar lemma for projection onto submodules rather than affine subspaces already exists.)
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Add a lemma that
orthogonalProjection s₁ (orthogonalProjection s₂ p) = orthogonalProjection s₁ pfors₁ ≤ s₂. (A similar lemma for projection onto submodules rather than affine subspaces already exists.)