lemma A.7 Behaviour of a maximal consistent set
open in the book ·
appendices/A-long-proofs.tex:1597
· p. 2794
Rests on
-
depends_on
definition A.5
Maximal consistent
¶
-
depends_on
definition 3.82
Consistency, completeness, soundness
¶
- depends_on definition 3.80 Formal system ¶
- depends_on definition 3.7 Negation ¶
-
depends_on
definition 3.82
Consistency, completeness, soundness
¶
-
depends_on
proposition 3.22
Algebra of propositions
¶
-
depends_on
definition 3.17
Logical equivalence
¶
- depends_on definition 3.12 Biconditional ¶
- depends_on definition 3.14 Tautology ¶
- depends_on definition 3.6 Truth table ¶
- proves proof ch:01-logic-sets@proof-4 ¶
-
depends_on
definition 3.17
Logical equivalence
¶
- proves proof app:A-long-proofs@proof-5 ¶
Supports
-
depends_on
lemma A.11
Truth lemma
¶
-
depends_on
theorem A.12
Model existence
¶
- depends_on corollary A.14 Compactness ¶
- depends_on theorem A.13 Completeness ¶
-
depends_on
theorem A.12
Model existence
¶
-
depends_on
lemma A.10
lem:app-comp-welldefined
¶
- depends_on lemma A.11 Truth lemma ¶ ↺
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 |
→ | Maximal consistent | declared | appendices/A-long-proofs.tex:1612 |
depends_on |
→ | Algebra of propositions | declared | appendices/A-long-proofs.tex:1612 |
depends_on |
← | Truth lemma | declared | appendices/A-long-proofs.tex:1776 |
depends_on |
← | lem:app-comp-welldefined | declared | appendices/A-long-proofs.tex:1739 |
proves |
← | app:A-long-proofs@proof-5 | declared | appendices/A-long-proofs.tex:1615 |