lemma A.42 $(\R, +)$ is an ordered abelian group
open in the book ·
appendices/A-long-proofs.tex:2999
· p. 2810
Rests on
- depends_on definition A.41 Addition ¶
- depends_on definition A.38 Order on $\R$ ¶
-
depends_on
lemma A.37
Elementary properties of cuts
¶
- depends_on definition A.36 Cut ¶ ↺
- proves proof app:A-long-proofs@proof-27 ¶
- proves proof app:A-long-proofs@proof-30 ¶
Supports
- depends_on lemma A.44 $\R$ is an ordered field ¶
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 |
→ | Addition | declared | appendices/A-long-proofs.tex:3005 |
depends_on |
→ | Order on $\R$ | declared | appendices/A-long-proofs.tex:3005 |
depends_on |
→ | Elementary properties of cuts | declared | appendices/A-long-proofs.tex:3005 |
depends_on |
← | $\R$ is an ordered field | declared | appendices/A-long-proofs.tex:3053 |
proves |
← | app:A-long-proofs@proof-30 | declared | appendices/A-long-proofs.tex:3008 |