Theorems · Theorem · order theory
Order.succ_le_iff
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : SuccOrder α] {a b : α} [NoMaxOrder α], Order.succ a ≤ b ↔ a < b- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderSuccOrderNoMaxOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- NoMaxOrderstatement and proof · cited by 340
- not_isMaxproof · cited by 46
- Order.succ_le_iff_of_not_isMaxproof · cited by 15
Cited by20
Results whose statement or proof uses this declaration.
- PSet.rank_lt_of_memproof · cited by 7
- Ordinal.isNormal_derivFamilyproof · cited by 5
- Cardinal.natCast_add_one_le_iffproof · cited by 5
- Ordinal.nat_lt_cardproof · cited by 4
- PSet.rank_le_iffproof · cited by 3
- Ordinal.omega0_leproof · cited by 2
- Ordinal.isSuccPrelimit_iff_omega0_dvdproof · cited by 2
- Cardinal.aleph_one_le_iffproof · cited by 2
- PSet.rank_powersetproof · cited by 2
- Ordinal.mul_add_div_mulproof · cited by 2
- Cardinal.cantor'proof · cited by 2
- WType.cardinalMk_le_max_aleph0_of_finite'proof · cited by 2