Theorems · Definition · logic and foundations
ONote.FundamentalSequenceProp
ONote → Option ONote ⊕ (ℕ → ONote) → Prop
The property satisfied by fundamentalSequence o:
* inl none means o = 0
* inl (some a) means o = succ a
* inr f means o is a limit ordinal and f is a strictly increasing sequence which converges to
o
- Defined in
- Mathlib.SetTheory.Ordinal.Notation
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ordinalproof · cited by 1,688
- Order.succproof · cited by 633
- Order.IsSuccLimitproof · cited by 255
- ONotestatement and proof · cited by 88
- ONote.reprproof · cited by 45
- ONote.NFproof · cited by 36
Cited by10
Results whose statement or proof uses this declaration.
- ONote.fastGrowingproof · cited by 10
- ONote.fundamentalSequence_has_propstatement and proof · cited by 5
- ONote.fastGrowing_defstatement and proof · cited by 3
- ONote.fastGrowing_succproof · cited by 3
- ONote.fastGrowing_zero'proof · cited by 1
- ONote.fastGrowing_limitproof · cited by 1
- ONote.fundamentalSequenceProp_inl_nonestatement · cited by 0
- ONote.fundamentalSequenceProp_inl_somestatement · cited by 0
- ONote.fundamentalSequenceProp_inrstatement · cited by 0
- ONote.fastGrowing.eq_defstatement and proof · cited by 0