Theorems · Theorem · logic and foundations
Ordinal.opow_pos
∀ {a : Ordinal.{u_1}} (b : Ordinal.{u_1}), 0 < a → 0 < a ^ b- Defined in
- Mathlib.SetTheory.Ordinal.Exponential
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- mul_posproof · cited by 374
- Order.IsSuccLimitproof · cited by 255
- pos_iff_ne_zeroproof · cited by 180
- Ordinal.opow_zeroproof · cited by 38
- Ordinal.limitRecOnproof · cited by 20
- Ordinal.opow_add_oneproof · cited by 9
- Order.IsSuccLimit.posproof · cited by 3
- Ordinal.lt_opow_of_isSuccLimitproof · cited by 2
Cited by22
Results whose statement or proof uses this declaration.
- Ordinal.isNormal_opowproof · cited by 37
- Ordinal.opow_ne_zeroproof · cited by 10
- Ordinal.opow_addproof · cited by 9
- ONote.NFBelow.repr_ltproof · cited by 7
- Ordinal.opow_mul_lt_opowproof · cited by 5
- ONote.fundamentalSequence_has_propproof · cited by 5
- ONote.omega0_le_oaddproof · cited by 5
- Ordinal.div_opow_log_ltproof · cited by 4
- Ordinal.isSuccLimit_opow_leftproof · cited by 1
- Ordinal.CNF.eval_ltproof · cited by 1
- ONote.repr_opow_aux₁proof · cited by 1
- ONote.repr_opow_aux₂proof · cited by 1