proposition A.132 The count

open in the book · appendices/A-long-proofs.tex:7419 · p. 2857

Rests on

depends_on proposition A.128 The ellipsoidal system separates ¶
- depends_on lemma A.126 Cartesian coordinates and scale factors ¶
  - depends_on definition A.125 Ellipsoidal coordinates ¶
    - depends_on definition A.116 Orthogonal curvilinear coordinates; scale factors ¶
      - depends_on definition 7.98 Functions of class $C^{1}$ ¶
      - depends_on equation 10.25 eq:pde-helmholtz-equation ¶
  - depends_on equation A.263 eq:app-stackel-orthogonality ¶
  - proves proof app:A-long-proofs@proof-78 ¶
- depends_on lemma A.127 Lagrange's interpolation identity ¶
  - depends_on equation A.287 eq:app-stackel-hi ¶
  - proves proof app:A-long-proofs@proof-79 ¶
- depends_on theorem A.120 Stäckel and Robertson conditions ¶
  - depends_on definition A.118 Simple separation of the Helmholtz equation ¶
    - depends_on definition A.116 Orthogonal curvilinear coordinates; scale factors ¶ ↺
    - depends_on lemma 10.28 The separation constant ¶
      - depends_on definition 10.2 Linear, semilinear, quasilinear ¶
      - proves proof ch:08-pdes@proof-9 ¶
  - depends_on lemma A.119 Cofactor identities ¶
    - depends_on equation A.267 eq:app-stackel-nondegenerate ¶
    - proves proof app:A-long-proofs@proof-75 ¶
  - depends_on lemma A.117 Laplacian in orthogonal coordinates ¶
    - depends_on definition A.116 Orthogonal curvilinear coordinates; scale factors ¶ ↺
    - depends_on theorem 7.133 Gauss ¶
      - depends_on definition 7.127 Simple regions ¶
      - depends_on remark 7.128 What the derivations below take as given ¶
      - depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
      - proves proof ch:05-real-analysis@proof-79 ¶
    - proves proof app:A-long-proofs@proof-74 ¶
  - proves proof app:A-long-proofs@proof-76 ¶
  - proves proof app:A-long-proofs@proof-77 ¶
- proves proof app:A-long-proofs@proof-80 ¶
depends_on theorem A.130 Quoted: separable systems are confocal-quadric systems ¶
proves proof app:A-long-proofs@proof-81 ¶

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type	direction	node	provenance	where
`depends_on`	→	The ellipsoidal system separates	declared	appendices/A-long-proofs.tex:7422
`depends_on`	→	Quoted: separable systems are confocal-quadric systems	declared	appendices/A-long-proofs.tex:7422
`proves`	←	app:A-long-proofs@proof-81	declared	appendices/A-long-proofs.tex:7425