Theorems · Theorem · order theory
Order.not_isSuccPrelimit_iff
∀ {α : Type u_1} [inst : LT α] {a : α}, ¬Order.IsSuccPrelimit a ↔ ∃ b, b ⋖ a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LT
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CovBystatement and proof · cited by 290
- Order.IsSuccPrelimitstatement · cited by 157
Cited by4
Results whose statement or proof uses this declaration.
- Order.not_isSuccPrelimit_iff_succ_eqproof · cited by 3
- SuccOrder.isOpen_singleton_of_not_isSuccPrelimitproof · cited by 1
- Order.Fill.continuous_someproof · cited by 1
- Order.not_isSuccPrelimit_iff_exists_covByproof · cited by 0