Theorems · Theorem · order theory
Order.succ_eq_iff_covBy
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : SuccOrder α] {a b : α} [NoMaxOrder α], Order.succ a = b ↔ a ⋖ b- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 and proof · cited by 633
- SuccOrderstatement and proof · cited by 574
- NoMaxOrderstatement and proof · cited by 340
- CovBystatement · cited by 290
- CovBy.succ_eqproof · cited by 8
- Order.covBy_succproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- SuccOrder.isOpen_singleton_iffproof · cited by 3
- toIocDiv_wcovBy_toIcoDivproof · cited by 2
- Order.covBy_iff_add_one_eqproof · cited by 2