Theorems · Theorem · logic and foundations
ONote.omega0_le_oadd
∀ (e : ONote) (n : ℕ+) (a : ONote), Ordinal.omega0 ^ e.repr ≤ (e.oadd n a).repr
- Defined in
- Mathlib.SetTheory.Ordinal.Notation
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- Ordinalstatement · cited by 1,688
- le_transproof · cited by 985
- PNatstatement and proof · cited by 392
- Ordinal.omega0statement and proof · cited by 197
- Nat.cast_leproof · cited by 159
- ONotestatement and proof · cited by 88
- le_self_addproof · cited by 68
- ONote.reprstatement and proof · cited by 45
- mul_le_mul_iff_right₀proof · cited by 38
Cited by5
Results whose statement or proof uses this declaration.
- ONote.NF.below_of_lt'proof · cited by 3
- ONote.oadd_posproof · cited by 1
- ONote.repr_opow_aux₁proof · cited by 1
- ONote.repr_opow_aux₂proof · cited by 1
- ONote.oadd_lt_oadd_1proof · cited by 0