Theorems · Theorem · order theory
Order.le_succ_iff_eq_or_le
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : SuccOrder α] {a b : α}, a ≤ Order.succ b ↔ a = Order.succ b ∨ a ≤ b- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderSuccOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Order.succstatement and proof · cited by 633
- SuccOrderstatement and proof · cited by 574
- IsMaxproof · cited by 372
- le_of_eqproof · cited by 366
- le_iff_eq_or_ltproof · cited by 20
- Order.lt_succ_iff_of_not_isMaxproof · cited by 17
- IsMax.succ_eqproof · cited by 7
Cited by6
Results whose statement or proof uses this declaration.
- partialSups_succproof · cited by 3
- StrictMonoOn.Iic_id_leproof · cited by 3
- Order.Iic_succproof · cited by 2
- Nat.le_succ_iff_eq_or_leproof · cited by 1
- Order.le_succ_bot_iffproof · cited by 1
- InverseSystem.isNatEquiv_piEquivSuccproof · cited by 0