Theorems · Theorem · order theory
Order.le_pred_iff_of_not_isMin
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : PredOrder α] {a b : α}, ¬IsMin a → (b ≤ Order.pred a ↔ b < a)- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- PredOrderstatement and proof · cited by 334
- IsMinstatement and proof · cited by 277
- Order.predstatement · cited by 273
- LT.lt.trans_le'proof · cited by 52
- Order.le_pred_of_ltproof · cited by 15
- Order.pred_lt_of_not_isMinproof · cited by 9
Cited by14
Results whose statement or proof uses this declaration.
- Order.pred_lt_iff_of_not_isMinproof · cited by 10
- Order.pred_le_predproof · cited by 5
- Order.IsPredPrelimit.lt_predproof · cited by 4
- Set.Icc_pred_right_eq_Ico_of_not_isMinproof · cited by 4
- Order.Iic_pred_of_not_isMinproof · cited by 3
- Order.le_pred_iffproof · cited by 3
- Set.Ioc_pred_right_eq_Iooproof · cited by 3
- Set.Iic_pred_eq_Iio_of_not_isMinproof · cited by 3
- MeasureTheory.IsStoppingTime.measurableSet_lt_of_predproof · cited by 1
- Order.le_pred_iff_of_not_isMin'proof · cited by 1
- Order.le_sub_one_iff_of_not_isMinproof · cited by 1
- Order.pred_lt_pred_iff_of_not_isMinproof · cited by 1