lemma A.175 Tightness makes the Helly limit proper

open in the book · appendices/A-long-proofs.tex:9108 · p. 2877

Rests on

depends_on definition A.174 Tightness ¶
- depends_on definition 11.21 Distribution function ¶
  - depends_on definition 11.20 Density ¶
    - depends_on definition 7.39 Darboux sums and the definite integral ¶
      - depends_on axiom 7.1 Completeness of $\R$ ¶
depends_on theorem A.173 Helly's selection theorem ¶
- depends_on definition 11.21 Distribution function ¶ ↺
- depends_on theorem 7.7 Bolzano–Weierstrass ¶
  - depends_on corollary A.45 Archimedean property and density of $\Q$ ¶
    - depends_on definition A.36 Cut ¶
    - depends_on theorem A.40 Least-upper-bound property ¶
      - depends_on definition A.36 Cut ¶ ↺
      - depends_on definition A.38 Order on $\R$ ¶
      - proves proof app:A-long-proofs@proof-29 ¶
    - proves proof app:A-long-proofs@proof-32 ¶
  - depends_on corollary A.46 Monotone convergence ¶
    - depends_on theorem A.40 Least-upper-bound property ¶ ↺
    - proves proof app:A-long-proofs@proof-33 ¶
  - proves proof ch:05-real-analysis@proof-4 ¶
- proves proof app:A-long-proofs@proof-101 ¶
proves proof app:A-long-proofs@proof-102 ¶

Nothing declares a dependency on this node yet.

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Tightness	declared	appendices/A-long-proofs.tex:9114
`depends_on`	→	Helly's selection theorem	declared	appendices/A-long-proofs.tex:9114
`proves`	←	app:A-long-proofs@proof-102	declared	appendices/A-long-proofs.tex:9117