Theorems · Theorem · order theory
Order.succ_le_of_lt
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : SuccOrder α] {a b : α}, a < b → Order.succ a ≤ b- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Order.succstatement · cited by 633
- SuccOrderstatement and proof · cited by 574
- SuccOrder.succ_le_of_ltproof · cited by 1
Cited by47
Results whose statement or proof uses this declaration.
- Order.succ_le_iff_of_not_isMaxproof · cited by 15
- Order.add_one_le_of_ltproof · cited by 13
- Cardinal.succ_natCastproof · cited by 9
- Order.le_of_lt_succproof · cited by 9
- Order.succ_le_succproof · cited by 7
- ONote.NFBelow.repr_ltproof · cited by 7
- LT.lt.succ_leproof · cited by 5
- Cardinal.lift_succproof · cited by 4
- Monotone.pairwise_disjoint_on_Ico_succproof · cited by 3
- Monotone.pairwise_disjoint_on_Ioc_succproof · cited by 3
- Order.wcovBy_succproof · cited by 3
- StrictMonoOn.Iic_id_leproof · cited by 3