Theorems · Theorem · logic and foundations
Ordinal.isPrincipal_add_opow_of_isPrincipal_add
∀ {a : Ordinal.{u_1}},
Ordinal.IsPrincipal (fun x1 x2 => x1 + x2) a →
∀ (b : Ordinal.{u_1}), Ordinal.IsPrincipal (fun x1 x2 => x1 + x2) (a ^ b)- Defined in
- Mathlib.SetTheory.Ordinal.Principal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangeproof · cited by 4,705
- Ordinalstatement and proof · cited by 1,688
- eq_or_neproof · cited by 1,117
- Ordinal.omega0proof · cited by 197
- Ordinal.IsPrincipalstatement and proof · cited by 92
- Ordinal.opow_zeroproof · cited by 38
- Ordinal.zero_opowproof · cited by 13
- Ordinal.isPrincipal_add_omega0_opowproof · cited by 7
- Ordinal.opow_mulproof · cited by 4
- Ordinal.isPrincipal_add_iff_zero_or_omega0_opowproof · cited by 3
- Ordinal.isPrincipal_add_oneproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Ordinal.principal_add_opow_of_principal_addproof · cited by 0