One Jet Bundle model space chart At
oneJetBundle_model_space_chartAt
Plain-language statement
In the OneJetBundle to the model space, the charts are just the canonical identification between a product type and a bundle total space type, a.k.a. Bundle.TotalSpace.toProd.
Exact Lean statement
@[simp, mfld_simps]
theorem oneJetBundle_model_space_chartAt (p : OneJetBundle I H I' H') :
(chartAt π p).toPartialEquiv =
(Bundle.TotalSpace.toProd (H Γ H') (E βL[π] E')).toPartialEquivFormal artifact
Lean source
@[simp, mfld_simps]theorem oneJetBundle_model_space_chartAt (p : OneJetBundle I H I' H') : (chartAt π p).toPartialEquiv = (Bundle.TotalSpace.toProd (H Γ H') (E βL[π] E')).toPartialEquiv := by apply partialEquiv_eq_equiv Β· intro x rw [OpenPartialHomeomorph.coe_toPartialEquiv, oneJetBundle_chartAt_apply p x, inCoordinates_tangent_bundle_core_model_space] ext <;> rfl Β· simp_rw [oneJetBundle_chart_source, prodChartedSpace_chartAt, chartAt_self_eq, OpenPartialHomeomorph.refl_prod_refl] rfl Β· simp_rw [oneJetBundle_chart_target, prodChartedSpace_chartAt, chartAt_self_eq, OpenPartialHomeomorph.refl_prod_refl] rfl- Project
- Sphere eversion
- License
- Apache-2.0
- Commit
- ded8fda5e76b
- Source
- SphereEversion/Global/OneJetBundle.lean:607-621
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