Theorems · Theorem · order theory
Order.IsPredPrelimit.lt_pred
∀ {α : Type u_1} {a b : α} [inst : PartialOrder α] [inst_1 : PredOrder α],
Order.IsPredPrelimit b → b < a → b < Order.pred a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 21 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.
Cites9
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
- IsMinproof · cited by 277
- Order.predstatement and proof · cited by 273
- Order.IsPredPrelimitstatement and proof · cited by 93
- Order.le_pred_iff_of_not_isMinproof · cited by 14
- Order.IsPredPrelimit.isMinproof · cited by 7
- lt_iff_le_and_ne'proof · cited by 6
- IsMin.pred_eqproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- Order.IsPredPrelimit.lt_pred_iffproof · cited by 2
- Order.IsPredPrelimit.lt_sub_oneproof · cited by 1
- Order.isPredPrelimit_iff_lt_predproof · cited by 0
- Order.IsPredLimit.lt_predproof · cited by 0