Mathlib Map

Theorems · Theorem · logic and foundations

Ordinal.isNormal_opow

∀ {a : Ordinal.{u_1}}, 1 < a → Order.IsNormal fun x => a ^ x
Defined in
Mathlib.SetTheory.Ordinal.Exponential
Cited by
37 results in Mathlib
Foundations
Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

Ordinal.opow_add · cited by 9Ordinal.opow_addOrdinal.opow_le_iff_le_log · cited by 8Ordinal.opow_le_iff_le_logOrdinal.opow_lt_opow_iff_right · cited by 8Ordinal.opow_lt_opow_iff_…Ordinal.right_le_opow · cited by 4Ordinal.right_le_opowOrdinal.opow_mul · cited by 4Ordinal.opow_mulOrdinal.veblen_veblen_of_lt · cited by 4Ordinal.veblen_veblen_of_…Ordinal.veblen_zero_strictMono · cited by 4Ordinal.veblen_zero_stric…Ordinal.opow_le_opow_iff_right · cited by 3Ordinal.opow_le_opow_iff_…Ordinal.veblen_lt_veblen_iff_right · cited by 3Ordinal.veblen_lt_veblen_…Ordinal.veblen_pos · cited by 3Ordinal.veblen_posOrdinal.card_opow_le_of_omega0_le_left · cited by 3Ordinal.card_opow_le_of_o…Ordinal.isNormal_veblen_zero · cited by 2Ordinal.isNormal_veblen_z…Ordinal.veblen_add_one · cited by 2Ordinal.veblen_add_oneOrdinal.isSuccLimit_opow · cited by 2Ordinal.isSuccLimit_opowOrdinal.veblen_le_veblen_iff_right · cited by 2Ordinal.veblen_le_veblen_…Set.ofPred · cited by 6101Set.ofPredmul_one · cited by 3885mul_oneOrdinal · cited by 1688OrdinalLT.lt.ne' · cited by 1417lt.ne'Set.Iio · cited by 1166Set.Iiozero_lt_one · cited by 598zero_lt_oneLT.lt.trans · cited by 370lt.transOrder.IsSuccLimit · cited by 255Order.IsSuccLimitOrder.IsNormal · cited by 118Order.IsNormalmul_lt_mul_of_pos_left · cited by 71mul_lt_mul_of_pos_leftOrdinal.opow_pos · cited by 22Ordinal.opow_posOrdinal.opow_succ · cited by 11Ordinal.opow_succOrdinal.opow_le_of_isSuccLimit · cited by 7Ordinal.opow_le_of_isSucc…Order.IsNormal.of_succ_lt · cited by 4IsNormal.of_succ_ltOrdinal.isNormal_opowCITED BYCITES

Cites14

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

Cited by37

Results whose statement or proof uses this declaration.