[Merged by Bors] - feat(Geometry/Manifold/VectorBundle/Tangent): tangentCoordChange #8672
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Minor comment (here and elsewhere): a new rule in the style guide asks for a space after a left arrow. |
grunweg
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We define `tangentCoordChange` as a convenient abbreviation for coordinate changes on the tangent bundle. We also restate the axioms of `VectorBundleCore` as lemmas involving `extChartAt`. Currently, we need to write `(tangentBundleCore I M).coordChange (achart H x) (achart H y)`, referring explicitly to the atlas of `M`. Since `tangentBundleCore` uses the same base sets as the preferred charts of the base manifold, we wish to work directly with points `x y : M` and the preferred extended charts at those points (`extChartAt`). We find this definition and related lemmas useful in #8483 in shortening proofs.
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bors r+ |
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We define `tangentCoordChange` as a convenient abbreviation for coordinate changes on the tangent bundle. We also restate the axioms of `VectorBundleCore` as lemmas involving `extChartAt`. Currently, we need to write `(tangentBundleCore I M).coordChange (achart H x) (achart H y)`, referring explicitly to the atlas of `M`. Since `tangentBundleCore` uses the same base sets as the preferred charts of the base manifold, we wish to work directly with points `x y : M` and the preferred extended charts at those points (`extChartAt`). We find this definition and related lemmas useful in #8483 in shortening proofs.
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We define
tangentCoordChangeas a convenient abbreviation for coordinate changes on the tangent bundle. We also restate the axioms ofVectorBundleCoreas lemmas involvingextChartAt.Currently, we need to write
(tangentBundleCore I M).coordChange (achart H x) (achart H y), referring explicitly to the atlas ofM. SincetangentBundleCoreuses the same base sets as the preferred charts of the base manifold, we wish to work directly with pointsx y : Mand the preferred extended charts at those points (extChartAt).We find this definition and related lemmas useful in #8483 in shortening proofs.