Theorems · Theorem · order theory
Order.Icc_succ_left_of_not_isMax
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : SuccOrder α] {a b : α}, ¬IsMax a → Set.Icc (Order.succ a) b = Set.Ioc a b- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.Iccstatement · cited by 1,702
- Set.Iicproof · cited by 1,111
- Set.Iocstatement and proof · cited by 971
- Order.succstatement · cited by 633
- SuccOrderstatement and proof · cited by 574
- IsMaxstatement and proof · cited by 372
- Set.Ioi_inter_Iicproof · cited by 13
- Set.Ici_inter_Iicproof · cited by 12
- Order.Ici_succ_of_not_isMaxproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Order.Icc_succ_leftproof · cited by 2
- Set.insert_Ioc_succ_left_eq_Iocproof · cited by 2