Theorems · Theorem · order theory
Order.not_isSuccPrelimit_iff_succ_eq
∀ {α : Type u_1} {a : α} [inst : PartialOrder α] [inst_1 : SuccOrder α],
¬Order.IsSuccPrelimit a ↔ ∃ b, ¬IsMax b ∧ Order.succ b = a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 19 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.
Cites11
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
- IsMaxstatement and proof · cited by 372
- CovByproof · cited by 290
- Order.IsSuccPrelimitstatement · cited by 157
- CovBy.ltproof · cited by 51
- LT.lt.not_isMaxproof · cited by 11
- Order.covBy_succ_of_not_isMaxproof · cited by 8
- CovBy.succ_eqproof · cited by 8
- Order.not_isSuccPrelimit_iffproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Order.isSuccPrelimitRecOn_succ_of_not_isMaxproof · cited by 2
- SuccOrder.prelimitRecOn_succ_of_not_isMaxproof · cited by 2
- Order.mem_range_succ_of_not_isSuccPrelimitproof · cited by 1