Theorems · Theorem · order theory
Order.succ_le_iff_of_not_isMax
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : SuccOrder α] {a b : α}, ¬IsMax a → (Order.succ a ≤ b ↔ a < b)- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 15 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
- LT.lt.trans_leproof · cited by 678
- Order.succstatement · cited by 633
- SuccOrderstatement and proof · cited by 574
- IsMaxstatement and proof · cited by 372
- Order.succ_le_of_ltproof · cited by 42
- Order.lt_succ_of_not_isMaxproof · cited by 25
Cited by15
Results whose statement or proof uses this declaration.
- Order.one_le_iff_posproof · cited by 27
- Order.succ_le_iffproof · cited by 20
- Order.lt_succ_iff_of_not_isMaxproof · cited by 17
- Order.IsSuccPrelimit.succ_ltproof · cited by 7
- Order.succ_le_succproof · cited by 7
- Set.Ico_succ_left_eq_Iooproof · cited by 4
- Set.Ici_succ_eq_Ioi_of_not_isMaxproof · cited by 3
- strictMonoOn_Iic_of_lt_succproof · cited by 3
- Order.Ici_succ_of_not_isMaxproof · cited by 3
- Order.add_one_le_iff_of_not_isMaxproof · cited by 3
- Set.Icc_succ_left_eq_Ioc_of_not_isMaxproof · cited by 3
- Order.succ_le_iff_of_not_isMax'proof · cited by 2