lemma A.616 The four identities

open in the book · appendices/A-long-proofs.tex:29620 · p. 3088

Rests on

depends_on equation 26.24 eq:cd-c-matrix ¶
depends_on equation 22.46 eq:ham-jacobi ¶
depends_on proposition 25.4 Leibniz rule and derivations ¶
- depends_on definition 24.14 Hamiltonian vector field ¶
  - depends_on definition 24.8 Symplectic manifold ¶
    - depends_on definition 13.105 Closed form ¶
      - depends_on definition 13.103 Exterior derivative ¶
      - depends_on definition 13.98 $k$-form ¶
    - depends_on definition 13.98 $k$-form ¶ ↺
    - depends_on definition 24.2 Symplectic vector space ¶
      - depends_on proposition 5.119 Normal form of a non-degenerate antisymmetric form ¶
  - depends_on equation 22.4 eq:ham-pdot ¶
  - depends_on equation 22.3 eq:ham-qdot ¶
- depends_on theorem 25.3 The bracket is a Lie bracket ¶
  - depends_on equation 22.41 eq:ham-poisson-bracket ¶
  - depends_on equation 22.56 eq:ham-symplectic-matrix ¶
  - proves proof ch:08-poisson-quantum-bridge@proof-1 ¶
- proves proof ch:08-poisson-quantum-bridge@proof-2 ¶
proves proof app:A-long-proofs@proof-372 ¶

Supports

depends_on theorem A.617 Jacobi identity for the Dirac bracket ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	eq:cd-c-matrix	declared	appendices/A-long-proofs.tex:29637
`depends_on`	→	eq:ham-jacobi	declared	appendices/A-long-proofs.tex:29637
`depends_on`	→	Leibniz rule and derivations	declared	appendices/A-long-proofs.tex:29637
`depends_on`	←	Jacobi identity for the Dirac bracket	declared	appendices/A-long-proofs.tex:29694
`proves`	←	app:A-long-proofs@proof-372	declared	appendices/A-long-proofs.tex:29640