proposition 7.122 Product identities of the nabla calculus

open in the book · parts/02-mathematical-methods/05-real-analysis.tex:3996 · p. 253

Rests on

depends_on equation 7.134 eq:ana-epsilon-curl ¶
depends_on lemma 7.121 Contraction of two Levi-Civita symbols ¶
- depends_on equation 7.134 eq:ana-epsilon-curl ¶ ↺
- proves proof ch:05-real-analysis@proof-74 ¶
depends_on proposition 7.30 Leibniz rule ¶
- depends_on definition 7.12 Product of functions ¶
  - depends_on definition 7.9 Real function ¶
    - depends_on definition 3.43 Map ¶
      - depends_on definition 3.24 Quantifiers ¶
      - depends_on definition 3.28 Set ¶
- 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 7.16 Limit ¶
      - depends_on definition 7.2 Absolute value ¶
      - depends_on definition 7.9 Real function ¶ ↺
    - depends_on equation 7.7 eq:ana-limit-left ¶
    - depends_on equation 7.5 eq:ana-limit-right ¶
  - depends_on definition 7.26 Derivative of a function at a point ¶
    - depends_on definition 7.16 Limit ¶ ↺
    - depends_on definition 7.9 Real function ¶ ↺
  - depends_on proposition 7.6 Algebra of limits ¶
    - depends_on definition 7.4 Convergence ¶
      - depends_on definition 7.2 Absolute value ¶ ↺
    - depends_on proposition 7.3 Triangle inequality ¶
      - depends_on definition 7.2 Absolute value ¶ ↺
      - proves proof ch:05-real-analysis@proof-1 ¶
    - proves proof ch:05-real-analysis@proof-3 ¶
  - proves proof ch:05-real-analysis@proof-11 ¶
- depends_on proposition 7.6 Algebra of limits ¶ ↺
- proves proof ch:05-real-analysis@proof-14 ¶
proves proof ch:05-real-analysis@proof-75 ¶

Supports

Nothing declares a dependency on this node yet.

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:ana-epsilon-curl	declared	parts/02-mathematical-methods/05-real-analysis.tex:4035
`depends_on`	→	Contraction of two Levi-Civita symbols	declared	parts/02-mathematical-methods/05-real-analysis.tex:4035
`depends_on`	→	Leibniz rule	declared	parts/02-mathematical-methods/05-real-analysis.tex:4035
`proves`	←	ch:05-real-analysis@proof-75	declared	parts/02-mathematical-methods/05-real-analysis.tex:4039