remark 22.39 Poisson's theorem does not manufacture new constants

Rests on

• depends_on remark 22.31 The bracket is a Lie algebra structure ¶
  • depends_on definition 5.128 Derivation ¶
    • depends_on definition 5.121 Algebra ¶
      • depends_on definition 4.4 Internal binary operation; magma ¶
        • depends_on definition 4.3 Algebraic structure ¶
        • depends_on definition 4.2 Binary operation ¶
      • depends_on definition 4.33 Vector space ¶
        • depends_on definition 4.8 Commutativity; abelian structure ¶
        • depends_on definition 4.32 Field ¶
        • depends_on definition 4.31 Module ¶
    • depends_on definition 5.37 Linear transformation ¶
      • depends_on definition 4.33 Vector space ¶ ↺
  • depends_on definition 5.127 Lie algebra ¶
    • depends_on definition 5.121 Algebra ¶ ↺
  • depends_on proposition 22.30 Properties of the Poisson bracket ¶
    • depends_on equation 22.42 eq:ham-poisson-matrix ¶
    • depends_on lemma 22.20 The symplectic condition ¶
      • depends_on definition 5.135 The symplectic group ¶
        • depends_on definition 5.113 Non-degenerate form ¶
        • depends_on equation 5.138 eq:lin-bilinear-expansion ¶
        • depends_on proposition 5.119 Normal form of a non-degenerate antisymmetric form ¶
      • depends_on equation 22.18 eq:ham-generating ¶
      • depends_on proposition 7.105 Clairaut–Schwarz ¶
        • depends_on definition 7.20 Continuity at a point ¶
        • depends_on theorem 7.35 Mean value theorem ¶
        • proves proof ch:05-real-analysis@proof-64 ¶
      • proves proof ch:05-hamiltonian-mechanics@proof-7 ¶
    • depends_on proposition 7.105 Clairaut–Schwarz ¶ ↺
    • proves proof ch:05-hamiltonian-mechanics@proof-12 ¶
• depends_on theorem 22.38 Poisson's theorem ¶
  • depends_on equation 22.46 eq:ham-jacobi ¶
  • depends_on theorem 22.34 Evolution of a phase-space function ¶
    • depends_on equation 22.4 eq:ham-pdot ¶
    • depends_on equation 22.41 eq:ham-poisson-bracket ¶
    • depends_on equation 22.3 eq:ham-qdot ¶
    • proves proof ch:05-hamiltonian-mechanics@proof-14 ¶
  • proves proof ch:05-hamiltonian-mechanics@proof-17 ¶

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