Theorems · Inductive type · order theory
SuccOrder
(α : Type u_3) → [Preorder α] → Type u_3
Order equipped with a sensible successor function.
- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 574 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement · cited by 7,952
Cited by760
Results whose statement or proof uses this declaration.
- Order.succstatement and proof · cited by 633
- Order.le_succstatement and proof · cited by 96
- IsSuccArchimedeanstatement · cited by 88
- CategoryTheory.TransfiniteCompositionOfShape.Fstatement and proof · cited by 47
- Order.lt_succstatement and proof · cited by 45
- Order.succ_le_of_ltstatement and proof · cited by 42
- CategoryTheory.TransfiniteCompositionOfShapestatement · cited by 32
- HomotopicalAlgebra.ReedyStructurestatement · cited by 30
- WithBot.succstatement and proof · cited by 30
- CategoryTheory.SmallObject.SuccStruct.Iterationstatement · cited by 29
- CategoryTheory.MorphismProperty.transfiniteCompositionsOfShapestatement and proof · cited by 25
- Order.lt_succ_of_not_isMaxstatement and proof · cited by 25
Showing the 200 most cited of 760.