Theorems · Theorem · logic and foundations
Ordinal.pred_le_iff_le_succ
∀ {a b : Ordinal.{u_4}}, a.pred ≤ b ↔ a ≤ Order.succ b- Defined in
- Mathlib.SetTheory.Ordinal.Arithmetic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangeproof · cited by 4,705
- Ordinalstatement and proof · cited by 1,688
- Order.succstatement and proof · cited by 633
- Order.IsSuccPrelimitproof · cited by 157
- Order.succ_eq_add_oneproof · cited by 115
- Ordinal.predstatement and proof · cited by 15
- Order.IsSuccPrelimit.ordinalPred_eqproof · cited by 5
- Ordinal.pred_add_oneproof · cited by 4
- Order.mem_range_succ_or_isSuccPrelimitproof · cited by 4
- Order.IsSuccPrelimit.le_succ_iffproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Ordinal.pred_succ_giproof · cited by 2
- Ordinal.lt_pred_iff_succ_ltproof · cited by 0