Theorems · Theorem · order theory
Order.isPredLimit_toDual_iff
∀ {α : Type u_1} {a : α} [inst : Preorder α], Order.IsPredLimit (OrderDual.toDual a) ↔ Order.IsSuccLimit a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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.
- DFunLike.coestatement and proof · cited by 62,936
- Equivstatement · cited by 8,337
- Preorderstatement and proof · cited by 7,952
- OrderDualstatement · cited by 927
- OrderDual.toDualstatement and proof · cited by 481
- Order.IsSuccLimitstatement · cited by 255
- Order.IsSuccPrelimitproof · cited by 157
- Order.IsPredLimitstatement · cited by 60
- not_isMin_iffproof · cited by 18
- Order.isPredLimit_iffproof · cited by 10
- Order.isSuccLimit_iffproof · cited by 9
- Order.isPredPrelimit_toDual_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Order.IsSuccLimit.dualproof · cited by 0