Theorems · Definition · logic and foundations
ONote.cmp
ONote → ONote → Ordering
Comparison of ordinal notations:
ω ^ e₁ * n₁ + a₁ is less than ω ^ e₂ * n₂ + a₂ when either e₁ < e₂, or e₁ = e₂ and
n₁ < n₂, or e₁ = e₂, n₁ = n₂, and a₁ < a₂.
- Defined in
- Mathlib.SetTheory.Ordinal.Notation
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ONotestatement and proof · cited by 88
- ONote.brecOnproof · cited by 12
Cited by9
Results whose statement or proof uses this declaration.
- ONote.cmp_comparesstatement · cited by 3
- ONote.repr_injproof · cited by 2
- ONote.addAuxproof · cited by 2
- ONote.TopBelowproof · cited by 1
- NONote.cmpproof · cited by 1
- ONote.cmp.eq_defstatement and proof · cited by 0
- NONote.cmp_comparesproof · cited by 0
- ONote.sub.eq_defstatement and proof · cited by 0
- ONote.eq_of_cmp_eqstatement and proof · cited by 0