Theorems · Theorem · logic and foundations
Ordinal.lt_omega0_opow_succ
∀ {a b : Ordinal.{u_1}}, a < Ordinal.omega0 ^ Order.succ b ↔ ∃ n, a < Ordinal.omega0 ^ b * ↑n- Defined in
- Mathlib.SetTheory.Ordinal.Exponential
- Cited by
- 1 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- le_reflproof · cited by 2,061
- Ordinalstatement and proof · cited by 1,688
- LT.lt.ne'proof · cited by 1,417
- LT.lt.trans_leproof · cited by 678
- Order.succstatement and proof · cited by 633
- zero_lt_oneproof · cited by 598
- le_imp_le_of_le_of_leproof · cited by 576
- LT.lt.transproof · cited by 370
- mul_le_mul'proof · cited by 274
- Ordinal.omega0statement and proof · cited by 197
- Order.lt_succproof · cited by 45
- Ordinal.natCast_lt_omega0proof · cited by 24
Cited by1
Results whose statement or proof uses this declaration.
- Ordinal.isPrincipal_add_iff_zero_or_omega0_opowproof · cited by 3