Theorems · Theorem · order theory
Order.le_iff_eq_or_succ_le
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : SuccOrder α] {a b : α}, a ≤ b ↔ a = b ∨ Order.succ a ≤ b- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderSuccOrder
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.
- PartialOrderstatement and proof · cited by 6,410
- Order.succstatement · 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.succ_le_iff_of_not_isMaxproof · cited by 15
- IsMax.succ_eqproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Order.le_iff_eq_or_succ_le'proof · cited by 0