Theorems · Theorem · order theory
Order.IsSuccPrelimit.succ_lt
∀ {α : Type u_1} {a b : α} [inst : PartialOrder α] [inst_1 : SuccOrder α],
Order.IsSuccPrelimit b → a < b → Order.succ a < b- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 7 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.
Cites9
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
- IsMaxproof · cited by 372
- Order.IsSuccPrelimitstatement and proof · cited by 157
- lt_iff_le_and_neproof · cited by 47
- Order.succ_le_iff_of_not_isMaxproof · cited by 15
- IsMax.succ_eqproof · cited by 7
- Order.IsSuccPrelimit.isMaxproof · cited by 7
Cited by7
Results whose statement or proof uses this declaration.
- Order.IsSuccLimit.succ_ltproof · cited by 18
- Cardinal.preBeth_limitproof · cited by 5
- Order.isSuccPrelimit_iff_succ_ltproof · cited by 4
- Ordinal.isSuccLimit_subproof · cited by 2
- Order.IsSuccPrelimit.succ_lt_iffproof · cited by 2
- Order.IsSuccPrelimit.add_one_ltproof · cited by 2
- Field.Emb.Cardinal.iSup_filtrationproof · cited by 0