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Theorems · Theorem · logic and foundations

Order.IsSuccPrelimit.ordinalPred_eq

∀ {o : Ordinal.{u_4}}, Order.IsSuccPrelimit o → o.pred = o

Alias of Ordinal.pred_eq_of_isSuccPrelimit.

Defined in
Mathlib.SetTheory.Ordinal.Arithmetic
Cited by
5 results in Mathlib
Foundations
Depth 38 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.pred_eq_iff_isSuccPrelimit · cited by 2Ordinal.pred_eq_iff_isSuc…Ordinal.pred_le_iff_le_succ · cited by 1Ordinal.pred_le_iff_le_su…Ordinal.pred_zero · cited by 0Ordinal.pred_zeroOrder.IsSuccLimit.ordinalPred_eq · cited by 0IsSuccLimit.ordinalPred_eqOrdinal.lift_pred · cited by 0Ordinal.lift_predOrdinal · cited by 1688OrdinalOrder.IsSuccPrelimit · cited by 157Order.IsSuccPrelimitOrdinal.pred · cited by 15Ordinal.predOrdinal.pred_eq_of_isSuccPrelimit · cited by 1Ordinal.pred_eq_of_isSucc…IsSuccPrelimit.ordinalPred_eqCITED BYCITES

Cites4

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

Cited by5

Results whose statement or proof uses this declaration.