Theorems · Theorem · logic and foundations
ONote.split_add_lt
∀ {o e : ONote} {n : ℕ+} {a : ONote} {m : ℕ} [o.NF], o.split = (e.oadd n a, m) → a.repr + ↑m < Ordinal.omega0 ^ e.repr- Defined in
- Mathlib.SetTheory.Ordinal.Notation
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ONote.NF
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ordinalstatement · cited by 1,688
- lt_of_lt_of_leproof · cited by 438
- PNatstatement and proof · cited by 392
- Ordinal.omega0statement and proof · cited by 197
- ONotestatement and proof · cited by 88
- ONote.reprstatement and proof · cited by 45
- ONote.NFstatement and proof · cited by 36
- Order.one_le_iff_ne_zeroproof · cited by 32
- Ordinal.natCast_lt_omega0proof · cited by 24
- Ordinal.opow_oneproof · cited by 14
- Ordinal.omega0_posproof · cited by 14
- ONote.splitstatement and proof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- ONote.repr_opowproof · cited by 1