Theorems · Theorem · order theory
not_isMin
∀ {α : Type u_1} [inst : Preorder α] [NoMinOrder α] (a : α), ¬IsMin a- Defined in
- Mathlib.Order.Max
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderNoMinOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- IsMinstatement · cited by 277
- NoMinOrderstatement and proof · cited by 247
- NoMinOrder.exists_ltproof · cited by 41
- not_isMin_iffproof · cited by 18
Cited by42
Results whose statement or proof uses this declaration.
- Order.pred_covByproof · cited by 4
- Order.pred_lt_iffproof · cited by 4
- Order.IsPredPrelimit.pred_neproof · cited by 3
- Order.le_pred_iffproof · cited by 3
- Order.Ioc_pred_leftproof · cited by 2
- Order.Ioi_predproof · cited by 2
- Order.Ioo_pred_leftproof · cited by 2
- Set.insert_Ioc_left_eq_Ioc_predproof · cited by 2
- Order.pred_ltproof · cited by 2
- PredOrder.isOpen_singleton_iffproof · cited by 2
- Order.Icc_pred_rightproof · cited by 1
- Set.Icc_pred_right_eq_Icoproof · cited by 1