Theorems · Inductive type · order theory
SuccAddOrder
(α : Type u_1) → [Preorder α] → [Add α] → [One α] → Type u_1
A typeclass for succ x = x + 1.
- Defined in
- Mathlib.Algebra.Order.SuccPred
- Cited by
- 108 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 4 definitions · uses no axioms
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 by114
Results whose statement or proof uses this declaration.
- Order.succ_eq_add_onestatement and proof · cited by 115
- Order.one_le_iff_ne_zerostatement and proof · cited by 32
- Order.one_le_iff_posstatement and proof · cited by 27
- Order.lt_one_iffstatement and proof · cited by 14
- Order.lt_add_one_iffstatement and proof · cited by 13
- Order.add_one_le_of_ltstatement and proof · cited by 13
- Finset.Ico_add_one_right_eq_Iccstatement and proof · cited by 10
- Order.le_one_iffstatement and proof · cited by 10
- Finset.insert_Ico_right_eq_Ico_add_onestatement and proof · cited by 8
- Order.add_one_le_iffstatement and proof · cited by 8
- Order.lt_two_iffstatement and proof · cited by 5
- Order.le_of_lt_add_onestatement and proof · cited by 4