Theorems · Theorem · logic and foundations
Ordinal.isPrincipal_add_omega0_opow
∀ (o : Ordinal.{u_1}), Ordinal.IsPrincipal (fun x1 x2 => x1 + x2) (Ordinal.omega0 ^ o)- Defined in
- Mathlib.SetTheory.Ordinal.Principal
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- add_zeroproof · cited by 2,707
- LT.lt.leproof · cited by 2,189
- Ordinalstatement and proof · cited by 1,688
- eq_or_neproof · cited by 1,117
- LT.lt.trans_leproof · cited by 678
- Nat.cast_addproof · cited by 586
- mul_addproof · cited by 413
- Ordinal.omega0statement and proof · cited by 197
- Ordinal.IsPrincipalstatement and proof · cited by 92
- Ordinal.opow_zeroproof · cited by 38
- add_lt_add_of_le_of_ltproof · cited by 31
- Ordinal.natCast_lt_omega0proof · cited by 24
Cited by7
Results whose statement or proof uses this declaration.
- Ordinal.add_of_omega0_opow_leproof · cited by 5
- Ordinal.isPrincipal_add_iff_zero_or_omega0_opowproof · cited by 3
- ONote.split_add_ltproof · cited by 1
- Ordinal.add_omega0_opowproof · cited by 1
- ONote.repr_opow_aux₂proof · cited by 1
- Ordinal.isPrincipal_add_opow_of_isPrincipal_addproof · cited by 1
- Ordinal.principal_add_omega0_opowproof · cited by 0