Theorems · Theorem · order theory
Order.IsSuccPrelimit.lt_iff_exists_lt
∀ {α : Type u_1} {a b : α} [inst : LinearOrder α], Order.IsSuccPrelimit b → (a < b ↔ ∃ c < b, a < c)- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- not_iff_notproof · cited by 159
- Order.IsSuccPrelimitstatement and proof · cited by 157
- Order.IsSuccPrelimit.le_iff_forall_leproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Order.IsSuccPrelimit.isLUB_Iioproof · cited by 3
- comap_coe_nhdsLT_of_Ioo_subsetproof · cited by 3
- ZFSet.vonNeumann_of_isSuccPrelimitproof · cited by 1
- Order.IsSuccLimit.lt_iff_exists_ltproof · cited by 1