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Theorems · Definition · logic and foundations

Ordinal.CNF.rec

(b : Ordinal.{u_2}) →
  {C : Ordinal.{u_2} → Sort u_1} →
    C 0 → ((o : Ordinal.{u_2}) → o ≠ 0 → C (o % b ^ Ordinal.log b o) → C o) → (o : Ordinal.{u_2}) → C o

Inducts on the base b expansion of an ordinal.

Defined in
Mathlib.SetTheory.Ordinal.CantorNormalForm
Cited by
7 results in Mathlib
Foundations
Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Ordinal.CNF · cited by 21Ordinal.CNFOrdinal.CNF.fst_le_log · cited by 2CNF.fst_le_logOrdinal.CNF.snd_pos · cited by 2CNF.snd_posOrdinal.CNF.sortedGT · cited by 2CNF.sortedGTOrdinal.CNF.foldr · cited by 1CNF.foldrOrdinal.CNF.rec_pos · cited by 1CNF.rec_posOrdinal.CNF.rec_zero · cited by 1CNF.rec_zeroOrdinal.CNF.snd_lt · cited by 0CNF.snd_ltOrdinal · cited by 1688OrdinalOrdinal.log · cited by 45Ordinal.logCNF.recCITED BYCITES

Cites2

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Cited by8

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