Theorems · Theorem · logic and foundations
Ordinal.opow_lt_opow_iff_right
∀ {a b c : Ordinal.{u_1}}, 1 < a → (a ^ b < a ^ c ↔ b < c)- Defined in
- Mathlib.SetTheory.Ordinal.Exponential
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 87 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
- StrictMono.lt_iff_ltproof · cited by 86
- Order.IsNormal.strictMonoproof · cited by 44
- Ordinal.isNormal_opowproof · cited by 37
Cited by8
Results whose statement or proof uses this declaration.
- ONote.fundamentalSequence_has_propproof · cited by 5
- ONote.NF.below_of_lt'proof · cited by 3
- Ordinal.left_lt_opowproof · cited by 2
- Ordinal.isPrincipal_add_of_isPrincipal_mul_opowproof · cited by 2
- Ordinal.one_lt_opowproof · cited by 1
- Ordinal.mul_lt_omega0_opowproof · cited by 1
- Ordinal.opow_eq_one_iffproof · cited by 1
- Ordinal.opow_dvd_opow_iffproof · cited by 0