Theorems · Theorem · order theory
not_isMax
∀ {α : Type u_1} [inst : Preorder α] [NoMaxOrder α] (a : α), ¬IsMax a- Defined in
- Mathlib.Order.Max
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderNoMaxOrder
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
- IsMaxstatement · cited by 372
- NoMaxOrderstatement and proof · cited by 340
- NoMaxOrder.exists_gtproof · cited by 62
- not_isMax_iffproof · cited by 24
Cited by46
Results whose statement or proof uses this declaration.
- Order.lt_succproof · cited by 45
- Order.lt_succ_iffproof · cited by 22
- Order.succ_le_iffproof · cited by 20
- Order.lt_add_one_iffproof · cited by 13
- Order.add_one_le_iffproof · cited by 8
- Order.covBy_succproof · cited by 6
- Order.Iio_succproof · cited by 4
- Order.IsSuccPrelimit.succ_neproof · cited by 3
- Order.Ico_succ_rightproof · cited by 3
- SuccOrder.isOpen_singleton_iffproof · cited by 3
- Order.Icc_succ_leftproof · cited by 2
- Set.Iio_succ_eq_Iicproof · cited by 2