lemma A.104 The recursion

open in the book · appendices/A-long-proofs.tex:6138 · p. 2844

Rests on

depends_on definition A.103 First-order quasilinear system with zero data ¶
- depends_on definition A.102 Normal Cauchy problem of order $k$ ¶
  - depends_on definition 10.1 Partial differential equation; order ¶
    - depends_on definition 7.98 Functions of class $C^{1}$ ¶
      - depends_on definition 7.20 Continuity at a point ¶
      - depends_on definition 7.97 Partial derivative; gradient ¶
    - depends_on definition 6.2 Open set ¶
      - depends_on definition 6.1 Topological space ¶
  - depends_on proposition 10.11 What a characteristic surface is ¶
    - depends_on definition 10.10 Characteristic surface ¶
      - depends_on definition 10.4 The second-order operator ¶
      - depends_on definition 10.3 Principal part and principal symbol ¶
    - depends_on theorem 10.8 The type is a coordinate invariant ¶
      - depends_on definition 10.6 Type of a second-order operator ¶
      - depends_on proposition 7.31 Chain rule ¶
      - depends_on theorem 5.116 Sylvester's law of inertia ¶
      - proves proof ch:08-pdes@proof-1 ¶
    - proves proof ch:08-pdes@proof-2 ¶
- depends_on definition 10.2 Linear, semilinear, quasilinear ¶
  - depends_on definition 10.1 Partial differential equation; order ¶ ↺
depends_on equation 10.2 eq:pde-multi-index ¶
proves proof app:A-long-proofs@proof-67 ¶

Supports

depends_on lemma A.109 Domination ¶
- depends_on theorem A.112 Cauchy–Kovalevskaya, first-order form ¶
depends_on lemma A.105 Formal reduction of a normal problem ¶

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`	→	First-order quasilinear system with zero data	declared	appendices/A-long-proofs.tex:6156
`depends_on`	→	eq:pde-multi-index	declared	appendices/A-long-proofs.tex:6156
`depends_on`	←	Domination	declared	appendices/A-long-proofs.tex:6341
`depends_on`	←	Formal reduction of a normal problem	declared	appendices/A-long-proofs.tex:6212
`proves`	←	app:A-long-proofs@proof-67	declared	appendices/A-long-proofs.tex:6159