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Theorems · Theorem · logic and foundations

Ordinal.one_lt_opow

∀ {a b : Ordinal.{u_1}}, 1 < a ^ b ↔ 1 < a ∧ b ≠ 0
Defined in
Mathlib.SetTheory.Ordinal.Exponential
Cited by
1 results in Mathlib
Foundations
Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Ordinal.one_lt_pow · cited by 0Ordinal.one_lt_powOrdinal · cited by 1688Ordinalpos_iff_ne_zero · cited by 180pos_iff_ne_zeroOrdinal.opow_zero · cited by 38Ordinal.opow_zeroOrder.le_one_iff · cited by 10Order.le_one_iffOrdinal.one_opow · cited by 9Ordinal.one_opowOrdinal.opow_lt_opow_iff_right · cited by 8Ordinal.opow_lt_opow_iff_…Ordinal.zero_opow_le · cited by 1Ordinal.zero_opow_leOrdinal.one_lt_opowCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.