lemma A.19 Numerals behave

open in the book · appendices/A-long-proofs.tex:2042 · p. 2800

Rests on

depends_on definition 3.83 Peano arithmetic ¶
- depends_on axiom 3.33 Peano axioms ¶
- depends_on axiom 3.34 Principle of induction ¶
- depends_on definition 3.80 Formal system ¶
depends_on equation A.118 eq:app-inc-Q-successor ¶
depends_on equation A.119 eq:app-inc-order ¶
proves proof app:A-long-proofs@proof-13 ¶

depends_on lemma A.24 lem:app-inc-beta-delta0 ¶
- depends_on theorem A.25 thm:app-inc-primrec ¶
  - depends_on theorem A.17 Representability ¶
    - depends_on proposition A.28 prop:app-inc-derivability ¶
      - depends_on theorem A.29 Second incompleteness theorem ¶
    - depends_on theorem A.30 Church, Turing ¶
    - depends_on theorem A.26 Diagonal lemma ¶
      - depends_on theorem A.27 Rosser ¶
    - depends_on theorem A.27 Rosser ¶ ↺
depends_on lemma A.20 $\Sigma_{1}$-completeness ¶
- depends_on theorem A.25 thm:app-inc-primrec ¶ ↺
- depends_on theorem A.17 Representability ¶ ↺
depends_on theorem A.25 thm:app-inc-primrec ¶ ↺
depends_on theorem A.27 Rosser ¶ ↺

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Peano arithmetic	declared	appendices/A-long-proofs.tex:2059
`depends_on`	→	eq:app-inc-Q-successor	declared	appendices/A-long-proofs.tex:2059
`depends_on`	→	eq:app-inc-order	declared	appendices/A-long-proofs.tex:2059
`depends_on`	←	lem:app-inc-beta-delta0	declared	appendices/A-long-proofs.tex:2210
`depends_on`	←	$\Sigma_{1}$-completeness	declared	appendices/A-long-proofs.tex:2110
`depends_on`	←	thm:app-inc-primrec	declared	appendices/A-long-proofs.tex:2229
`depends_on`	←	Rosser	declared	appendices/A-long-proofs.tex:2428
`proves`	←	app:A-long-proofs@proof-13	declared	appendices/A-long-proofs.tex:2062