[Merged by Bors] - feat(Geometry/Euclidean/Altitude): map and restrict lemmas#32021
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jsm28 wants to merge 33 commits intoleanprover-community:masterfrom
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[Merged by Bors] - feat(Geometry/Euclidean/Altitude): map and restrict lemmas#32021jsm28 wants to merge 33 commits intoleanprover-community:masterfrom
map and restrict lemmas#32021jsm28 wants to merge 33 commits intoleanprover-community:masterfrom
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…_direction_map` Add an instance that affine maps send finite-dimensional subspaces to finite-dimensional subspaces.
…f_injective`
Add a lemma
```lean
lemma comap_map_eq_of_injective (f : P₁ →ᵃ[k] P₂) (hf : Function.Injective f)
(s : AffineSubspace k P₁) : (s.map f).comap f = s :=
```
deduced from a `GaloisCoinsertion` as is done for such a lemma for
some other subobject types.
Add the lemma ```lean lemma map_vectorSpan (s : Set P₁) : (vectorSpan k s).map f.linear = vectorSpan k (f '' s) := by ``` analogous to `map_span` which we have for `affineSpan`.
Add lemmas about mapping `orthogonalProjection`, `reflection` and `orthogonalProjectionSpan` under an affine isometry, and in particular mapping from a subspace to the full space.
Add lemmas about `altitude`, `altitudeFoot` and `height` for simplices mapped under an affine isometry or restricted to an affine subspace.
PR summary bb55063693Import changes for modified filesNo significant changes to the import graph Import changes for all files
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Co-authored-by: Ruben Van de Velde <[email protected]>
Co-authored-by: Ruben Van de Velde <[email protected]>
Co-authored-by: Oliver Nash <[email protected]>
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bors d+
Please check you're happy with the new lemma and deprecation I added before merging
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Add lemmas about `altitude`, `altitudeFoot` and `height` for simplices mapped under an affine isometry or restricted to an affine subspace. Moves: - `Submodule.map_orthogonal` -> `Submodule.map_orthogonal_equiv` Co-authored-by: Eric Wieser <[email protected]>
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map and restrict lemmasmap and restrict lemmas
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…rover-community#32021) Add lemmas about `altitude`, `altitudeFoot` and `height` for simplices mapped under an affine isometry or restricted to an affine subspace. Moves: - `Submodule.map_orthogonal` -> `Submodule.map_orthogonal_equiv` Co-authored-by: Eric Wieser <[email protected]>
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Add lemmas about
altitude,altitudeFootandheightfor simplices mapped under an affine isometry or restricted to an affine subspace.Moves:
Submodule.map_orthogonal->Submodule.map_orthogonal_equivfiniteDimensional_direction_map#32016comap_map_eq_of_injective#32017mapand subtype lemmas #32019