Rel Mfld Ample localize
RelMfld.Ample.localize
Plain-language statement
Ampleness survives localization
Exact Lean statement
theorem RelMfld.Ample.localize (hR : R.Ample) : (R.localize φ ψ).Ample
Formal artifact
Lean source
theorem RelMfld.Ample.localize (hR : R.Ample) : (R.localize φ ψ).Ample := by intro x p have : (RelMfld.localize φ ψ R).slice x p = (ψ.fderiv x.1.2).symm '' R.slice (φ.transfer ψ x) (p.map (φ.fderiv x.1.1)) := by ext v simp_rw [RelMfld.localize, ContinuousLinearEquiv.image_symm_eq_preimage, mem_preimage, mem_slice, mem_preimage] -- Porting note: the next `rw` should be part of the `simp_rw` above rw [mem_slice] dsimp only [OpenSmoothEmbedding.transfer, OneJetBundle.map, oneJetBundle_mk_fst, oneJetBundle_mk_snd] simp_rw [p.map_update_comp_right, ← p.update_comp_left, OneJetBundle.mk, ← ψ.fderiv_coe] rfl rw [this] exact (hR _).image ((ψ.fderiv x.1.2).symm).toContinuousAffineEquiv- Project
- Sphere eversion
- License
- Apache-2.0
- Commit
- ded8fda5e76b
- Source
- SphereEversion/Global/Relation.lean:522-537
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Person-level attribution pending.
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Source project: Sphere eversion
Person-level attribution pending.
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Project documentation
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Source project: Sphere eversion
Person-level attribution pending.