Prove2Me

Radial contact curve derivative

Proved
BirkhoffGlobalSection.radial_contact_curve_derivative

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

differential-geometryreal-analysis

Along two differentiable phase curves, the radial contact pairing obeys the bilinear product-rule derivative formula.

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

Preamble
import Theorems.Thm_BirkhoffGlobalSection_contact_variation_preservation_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.radial_contact_curve_derivative :
∀ (q v : ℝ → Phase) (t : ℝ) (a b : Phase)
    (hq : HasDerivAt q a t) (hv : HasDerivAt v b t),
    HasDerivAt (fun s => phaseRadialContact (q s) (v s))
      (phaseRadialContact a (v t) + phaseRadialContact (q t) b) t := by sorry
Source
Independent extraction of component 1 of the Proved theorem BirkhoffGlobalSection.contact_variation_preservation_bundle. Original verified source: Solutions/Sol_BirkhoffGlobalSection_contact_variation_preservation_bundle.lean. Exact original component retained.

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