Theorems · Theorem · logic and foundations
Ordinal.mul_lt_omega0_opow
∀ {a b c : Ordinal.{u}}, 0 < c → a < Ordinal.omega0 ^ c → b < Ordinal.omega0 → a * b < Ordinal.omega0 ^ c- Defined in
- Mathlib.SetTheory.Ordinal.Principal
- 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.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangeproof · cited by 4,705
- le_reflproof · cited by 2,061
- Ordinalstatement and proof · cited by 1,688
- mul_assocproof · cited by 1,667
- le_of_ltproof · cited by 1,175
- LE.le.trans_ltproof · cited by 795
- Order.succproof · cited by 633
- mul_le_mul'proof · cited by 274
- Order.IsSuccLimitproof · cited by 255
- Ordinal.omega0statement and proof · cited by 197
- lt_irreflproof · cited by 190
- mul_lt_mul_of_pos_leftproof · cited by 71
Cited by1
Results whose statement or proof uses this declaration.
- ONote.repr_opow_aux₂proof · cited by 1