lemma A.6 Lindenbaum

open in the book · appendices/A-long-proofs.tex:1558 · 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 proposition 3.67 Countability of the plane of naturals ¶
- depends_on definition 3.65 Countable set ¶
  - depends_on axiom 3.33 Peano axioms ¶
  - depends_on definition 3.62 Equipotence ¶
    - depends_on definition 3.47 Bijective map ¶
    - depends_on definition 3.40 Cardinal ¶
- depends_on definition 3.47 Bijective map ¶ ↺
- depends_on definition 3.38 Ordered pair and Cartesian product ¶
- proves proof ch:01-logic-sets@proof-13 ¶
proves proof app:A-long-proofs@proof-4 ¶

Nothing declares a dependency on this node yet.

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Maximal consistent	declared	appendices/A-long-proofs.tex:1560
`depends_on`	→	Countability of the plane of naturals	declared	appendices/A-long-proofs.tex:1560
`proves`	←	app:A-long-proofs@proof-4	declared	appendices/A-long-proofs.tex:1563