Theorems · Theorem · order theory
Order.lt_succ_iff_of_not_isMax
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : SuccOrder α] {a b : α}, ¬IsMax a → (b < Order.succ a ↔ b ≤ a)- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderSuccOrder
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.
- LinearOrderstatement and proof · cited by 8,572
- Order.succstatement · cited by 633
- SuccOrderstatement and proof · cited by 574
- IsMaxstatement and proof · cited by 372
- Order.succ_le_iff_of_not_isMaxproof · cited by 15
Cited by17
Results whose statement or proof uses this declaration.
- Order.lt_succ_iffproof · cited by 22
- Order.le_succ_iff_eq_or_leproof · cited by 6
- Set.Ioo_succ_right_eq_Ioc_of_not_isMaxproof · cited by 4
- Order.lt_succ_iff_eq_or_lt_of_not_isMaxproof · cited by 3
- disjointed_succproof · cited by 3
- monotone_transfiniteIterateproof · cited by 3
- Order.Iio_succ_of_not_isMaxproof · cited by 3
- Set.Iio_succ_eq_Iic_of_not_isMaxproof · cited by 3
- Set.Ico_succ_right_eq_Icc_of_not_isMaxproof · cited by 3
- Order.lt_one_iff_nonposproof · cited by 2
- Order.lt_add_one_iff_of_not_isMaxproof · cited by 2
- Order.succ_le_succ_iff_of_not_isMaxproof · cited by 1