Theorems · Theorem · order theory
Order.pred_eq_csSup
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] [inst_1 : PredOrder α] [NoMinOrder α] (a : α),
Order.pred a = sSup (Set.Iio a)- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- le_of_ltproof · cited by 1,175
- Set.Iiostatement · cited by 1,166
- SupSet.sSupstatement · cited by 954
- ConditionallyCompleteLatticestatement and proof · cited by 364
- PredOrderstatement and proof · cited by 334
- Order.predstatement · cited by 273
- NoMinOrderstatement and proof · cited by 247
- LE.le.antisymm'proof · cited by 104
- le_csSupproof · cited by 66
- csSup_leproof · cited by 35
- Order.le_pred_of_ltproof · cited by 15
- Set.nonempty_Iioproof · cited by 10
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.