axiom 3.34 Principle of induction

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Supports

• depends_on definition 3.83 Peano arithmetic ¶
  • depends_on lemma A.19 Numerals behave ¶
    • 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 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 ¶
  • depends_on lemma 3.86 Diagonal lemma ¶
    • depends_on theorem 3.87 Gödel, 1931 ¶
      • depends_on theorem A.29 Second incompleteness theorem ¶
      • depends_on theorem 3.88 Gödel's second incompleteness theorem ¶
    • depends_on theorem 3.91 Tarski's undefinability of truth ¶
  • depends_on theorem 3.88 Gödel's second incompleteness theorem ¶ ↺
• depends_on lemma 7.64 Well-ordering of $\N$ ¶
  • depends_on lemma 7.65 The integer part ¶
    • depends_on lemma 7.67 The limit over real exponents ¶
      • depends_on proposition 7.68 The natural base ¶
        • depends_on remark 7.70 What the condition says ¶
    • depends_on proposition 7.77 Special values, periodicity, and the kernel ¶
      • depends_on lemma 7.78 Chord, arc, tangent ¶
        • depends_on proposition 7.79 The polygon recursion ¶
      • depends_on proposition 7.85 Irrationality of $\pi$ ¶
        • depends_on remark 7.94 Three numbers, two kinds ¶
        • depends_on remark 7.87 Priority, and what irrationality does not give ¶
      • depends_on proposition 7.79 The polygon recursion ¶ ↺
      • depends_on proposition 7.83 Viète's product ¶
        • depends_on remark 7.84 One construction, two faces ¶
      • depends_on proposition 125.2 Crystallographic restriction ¶
        • depends_on remark 125.3 What the theorem does and does not forbid ¶
      • depends_on remark 7.88 $\pi$ elsewhere in this treatise ¶
    • depends_on proposition 7.89 Irrationality of square roots ¶
      • depends_on proposition 7.91 The golden ratio ¶
        • depends_on proposition 7.92 Continued fraction and the Fibonacci ratios ¶
        • depends_on proposition 125.2 Crystallographic restriction ¶ ↺
        • depends_on remark 7.95 Where $\varphi$ is used ¶
        • depends_on remark 7.94 Three numbers, two kinds ¶ ↺
  • depends_on proposition 7.89 Irrationality of square roots ¶ ↺
• depends_on proposition 3.42 Cardinal of the power set ¶
• depends_on theorem A.4 Soundness ¶
  • depends_on corollary A.14 Compactness ¶
  • depends_on theorem A.13 Completeness ¶