proposition 31.7 The three coincide in steady flow

open in the book · parts/03-classical-mechanics/14-fluid-dynamics.tex:186 · p. 1043

Rests on

depends_on definition 31.6 Streamline, pathline, streakline ¶
- depends_on definition 31.4 Material derivative ¶
  - depends_on equation 7.124 eq:ana-nabla-gradient ¶
  - depends_on proposition 7.104 Chain rule in several variables ¶
    - depends_on definition 7.13 Composite function ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on definition 7.99 Differentiability at a point ¶
      - depends_on definition 7.16 Limit ¶
      - depends_on definition 5.37 Linear transformation ¶
      - depends_on equation 6.12 eq:top-euclidean-metric ¶
    - depends_on definition 7.102 Differential of a function ¶
      - depends_on definition 7.99 Differentiability at a point ¶ ↺
      - depends_on definition 7.97 Partial derivative; gradient ¶
    - proves proof ch:05-real-analysis@proof-63 ¶
  - proves proof ch:14-fluid-dynamics@proof-1 ¶
proves proof ch:14-fluid-dynamics@proof-2 ¶

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type	direction	node	provenance	where
`depends_on`	→	Streamline, pathline, streakline	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:191
`proves`	←	ch:14-fluid-dynamics@proof-2	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:194