Theorems · Theorem · order theory
Order.not_isPredPrelimit_iff_pred_eq
∀ {α : Type u_1} {a : α} [inst : PartialOrder α] [inst_1 : PredOrder α],
¬Order.IsPredPrelimit a ↔ ∃ b, ¬IsMin b ∧ Order.pred b = a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderPredOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- PredOrderstatement and proof · cited by 334
- CovByproof · cited by 290
- IsMinstatement and proof · cited by 277
- Order.predstatement and proof · cited by 273
- Order.IsPredPrelimitstatement · cited by 93
- CovBy.ltproof · cited by 51
- Order.pred_covBy_of_not_isMinproof · cited by 8
- LT.lt.not_isMinproof · cited by 8
- CovBy.pred_eqproof · cited by 8
- Order.not_isPredPrelimit_iffproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Order.isPredPrelimitRecOn_pred_of_not_isMinproof · cited by 2
- PredOrder.prelimitRecOn_pred_of_not_isMinproof · cited by 2
- Order.mem_range_pred_of_not_isPredPrelimitproof · cited by 1