Theorems · Theorem · order theory
Order.le_succ
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : SuccOrder α] (a : α), a ≤ Order.succ a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 96 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 7 definitions · 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.le_succproof · cited by 1
Cited by124
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.RelativeCellComplex.attachCellsstatement · cited by 15
- Order.succ_eq_iff_isMaxproof · cited by 11
- Succ.recstatement and proof · cited by 10
- Order.succ_le_succproof · cited by 7
- CategoryTheory.SmallObject.SuccStruct.extendToSuccObjIsostatement · cited by 6
- Cardinal.isRegular_succproof · cited by 6
- Order.le_succ_iterateproof · cited by 5
- CategoryTheory.SmallObject.SuccStruct.extendToSucc.objIsostatement · cited by 5
- CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIsostatement · cited by 5
- Set.Ico_succ_left_eq_Iooproof · cited by 4
- strictMonoOn_of_lt_succproof · cited by 4
- reflTransGen_of_succ_of_leproof · cited by 4