One Jet Bundle chart source
oneJetBundle_chart_source
Plain-language statement
In J¹(M, M'), the source of a chart has a nice formula
Exact Lean statement
theorem oneJetBundle_chart_source (x₀ : J¹MM') :
(chartAt HJ x₀).source =
π (E →L[𝕜] E') FJ¹MM' ⁻¹' (chartAt (ModelProd H H') x₀.proj).sourceFormal artifact
Lean source
theorem oneJetBundle_chart_source (x₀ : J¹MM') : (chartAt HJ x₀).source = π (E →L[𝕜] E') FJ¹MM' ⁻¹' (chartAt (ModelProd H H') x₀.proj).source := by -- Porting note: was -- simp only [FiberBundle.chartedSpace_chartAt, trivializationAt_oneJetBundle_source, mfld_simps] rw [FiberBundle.chartedSpace_chartAt] simp_rw [ OpenPartialHomeomorph.trans_toPartialEquiv, PartialEquiv.trans_source, OpenPartialHomeomorph.prod_toPartialHomeomorph, PartialEquiv.prod_source, OpenPartialHomeomorph.coe_toPartialEquiv, Trivialization.coe_coe, OpenPartialHomeomorph.refl_partialEquiv, PartialEquiv.refl_source, prodChartedSpace_chartAt, OpenPartialHomeomorph.prod_toPartialHomeomorph, trivializationAt_oneJetBundle_source, PartialEquiv.prod_source, Set.preimage_inter, prod_univ, ← preimage_inter, ← Set.prod_eq, preimage_preimage, inter_eq_left, subset_def, mem_preimage] intro x hx simpa- Project
- Sphere eversion
- License
- Apache-2.0
- Commit
- ded8fda5e76b
- Source
- SphereEversion/Global/OneJetBundle.lean:235-258
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