Theorems · Theorem · order theory
Order.succ_le_succ
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : SuccOrder α] {a b : α}, a ≤ b → Order.succ a ≤ Order.succ b- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- LE.le.transproof · cited by 3,151
- LT.lt.trans_leproof · cited by 678
- Order.succstatement and proof · cited by 633
- SuccOrderstatement and proof · cited by 574
- IsMaxproof · cited by 372
- Order.le_succproof · cited by 96
- Order.succ_le_of_ltproof · cited by 42
- LE.le.lt_of_not_geproof · cited by 21
- Order.succ_le_iff_of_not_isMaxproof · cited by 15
- Order.lt_succ_of_le_of_not_isMaxproof · cited by 4
- IsMax.monoproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- Order.succ_monoproof · cited by 4
- StrictMonoOn.Iic_id_leproof · cited by 3
- WithBot.succ_monoproof · cited by 1
- Order.pred_le_iff_le_succproof · cited by 1
- Order.bot_lt_succproof · cited by 1
- Order.le_succ_iff_pred_leproof · cited by 0
- Ordinal.blsub_succ_of_monoproof · cited by 0