proposition A.755 The Boussinesq pair

open in the book · appendices/A-long-proofs.tex:36759 · p. 3162

Rests on

depends_on equation A.1225 eq:app-fluid-kdv-nd-kin ¶
depends_on lemma A.754 Exact depth expansion ¶
- depends_on equation A.1224 eq:app-fluid-kdv-nd-laplace ¶
- depends_on theorem 7.38 Taylor's theorem with Lagrange remainder ¶
  - depends_on proposition 7.30 Leibniz rule ¶
    - depends_on definition 7.12 Product of functions ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on equation 7.14 eq:ana-derivh ¶
    - depends_on proposition 7.27 Differentiable implies continuous ¶
      - depends_on definition 7.20 Continuity at a point ¶
      - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on proposition 7.6 Algebra of limits ¶
      - proves proof ch:05-real-analysis@proof-11 ¶
    - depends_on proposition 7.6 Algebra of limits ¶ ↺
    - proves proof ch:05-real-analysis@proof-14 ¶
  - depends_on theorem 7.34 Rolle ¶
    - depends_on lemma 7.33 Fermat: interior extremum ¶
      - depends_on definition 7.26 Derivative of a function at a point ¶ ↺
      - depends_on proposition 7.18 Two-sided limit from one-sided limits ¶
      - proves proof ch:05-real-analysis@proof-17 ¶
    - depends_on theorem 7.24 Extreme value theorem ¶
      - depends_on axiom 7.1 Completeness of $\R$ ¶
      - depends_on proposition 7.22 Sequential characterization ¶
      - depends_on theorem 7.7 Bolzano–Weierstrass ¶
      - proves proof ch:05-real-analysis@proof-9 ¶
    - proves proof ch:05-real-analysis@proof-18 ¶
  - proves proof ch:05-real-analysis@proof-22 ¶
- proves proof app:A-long-proofs@proof-440 ¶
proves proof app:A-long-proofs@proof-441 ¶

Supports

depends_on theorem A.756 The Korteweg–de Vries equation ¶

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:app-fluid-kdv-nd-kin	declared	appendices/A-long-proofs.tex:36773
`depends_on`	→	Exact depth expansion	declared	appendices/A-long-proofs.tex:36773
`depends_on`	←	The Korteweg–de Vries equation	declared	appendices/A-long-proofs.tex:36842
`proves`	←	app:A-long-proofs@proof-441	declared	appendices/A-long-proofs.tex:36776