Prove2Me

Hamiltonian contact frame properties

Proved
BirkhoffGlobalSection.hamiltonian_contact_frame_properties

by Mazecto · Oct 3, 2026 · Mathlib 0df444a (Lean v4.33.1)

differential-geometryreal-analysis

Under a positive radial Hamiltonian derivative, the two contact-frame vectors satisfy the displayed energy tangency and zero-contact identities.

All displayed regularity, tangency, normalization and supplied-data hypotheses of the exact formal statement are retained.

Preamble
import Theorems.Thm_BirkhoffGlobalSection_transverse_contact_frame_bundle
open BirkhoffGlobalSection Set Filter SignType
open scoped ContDiff Topology
set_option linter.unusedVariables false


set_option autoImplicit false
set_option maxHeartbeats 800000
Formal statement
theorem BirkhoffGlobalSection.hamiltonian_contact_frame_properties :
∀ (F : Phase → ℝ) (y : Phase)
    (hp : 0 < phaseRadialContact y (hamiltonianVectorField F y)) (i : Fin 2),
    fderiv ℝ F y (hamiltonianContactFrame F y i) = 0 ∧
      phaseRadialContact y (hamiltonianContactFrame F y i) = 0 := by sorry
Source
Independent extraction of component 5 of the Proved theorem BirkhoffGlobalSection.transverse_contact_frame_bundle. Original verified source: Solutions/Sol_BirkhoffGlobalSection_transverse_contact_frame_bundle.lean. Exact original component retained.

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