Theorems · Theorem · logic and foundations
Ordinal.add_of_omega0_opow_le
∀ {a b c : Ordinal.{u}}, a < Ordinal.omega0 ^ b → Ordinal.omega0 ^ b ≤ c → a + c = c- Defined in
- Mathlib.SetTheory.Ordinal.Principal
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ordinalstatement and proof · cited by 1,688
- Ordinal.omega0statement and proof · cited by 197
- Ordinal.isPrincipal_add_omega0_opowproof · cited by 7
- Ordinal.IsPrincipal.add_eq_right_of_leproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Ordinal.preOmega_of_omega0_sq_leproof · cited by 1
- ONote.repr_opow_aux₂proof · cited by 1
- Cardinal.preBeth_of_omega0_sq_leproof · cited by 1
- Ordinal.isLeast_sub_lt_omega0_opow_logproof · cited by 0
- Ordinal.add_absorpproof · cited by 0