Theorems · Definition · logic and foundations
Ordinal.CNF
Ordinal.{u_1} → Ordinal.{u_1} → List (Ordinal.{u_1} × Ordinal.{u_1})The Cantor normal form of an ordinal o is the list of coefficients and exponents in the
base-b expansion of o.
We special-case CNF 0 o = CNF 1 o = [(0, o)] for o ≠ 0.
CNF b (b ^ u₁ * v₁ + b ^ u₂ * v₂) = [(u₁, v₁), (u₂, v₂)]
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ordinalstatement and proof · cited by 1,688
- Ordinal.logproof · cited by 45
- Ordinal.CNF.recproof · cited by 7
Cited by22
Results whose statement or proof uses this declaration.
- Ordinal.CNF.coeffproof · cited by 15
- Ordinal.CNF.zero_rightstatement · cited by 10
- Ordinal.CNF.ne_zerostatement · cited by 9
- Ordinal.CNF.coeff_of_notMem_CNFstatement and proof · cited by 5
- Ordinal.CNF.coeff_of_mem_CNFstatement and proof · cited by 3
- Ordinal.CNF.fst_le_logstatement and proof · cited by 2
- Ordinal.CNF.of_le_onestatement · cited by 2
- Ordinal.CNF.snd_posstatement and proof · cited by 2
- Ordinal.CNF.sortedGTstatement and proof · cited by 2
- Ordinal.CNF.support_coeffstatement and proof · cited by 2
- Ordinal.CNF.eval_coeffproof · cited by 1
- Ordinal.CNF.foldrstatement and proof · cited by 1