Theorems · Theorem · order theory
Order.IsSuccLimit.succ_lt
∀ {α : Type u_1} {a b : α} [inst : PartialOrder α] [inst_1 : SuccOrder α],
Order.IsSuccLimit b → a < b → Order.succ a < b- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 15 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.
Cites6
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 · cited by 633
- SuccOrderstatement and proof · cited by 574
- Order.IsSuccLimitstatement and proof · cited by 255
- Order.IsSuccLimit.isSuccPrelimitproof · cited by 37
- Order.IsSuccPrelimit.succ_ltproof · cited by 7
Cited by18
Results whose statement or proof uses this declaration.
- Order.IsNormal.of_succ_ltproof · cited by 4
- Ordinal.isNormal_preOmegaproof · cited by 3
- Ordinal.IsNormal.bsup_eqproof · cited by 2
- MeasurableSpace.generateMeasurable_eq_recproof · cited by 2
- Ordinal.bsup_eq_blsub_of_lt_succ_limitstatement and proof · cited by 2
- Cardinal.derivFamily_lt_ord_liftproof · cited by 2
- OrdinalApprox.lfpApprox_of_isSuccLimitproof · cited by 1
- Cardinal.isNormal_ordproof · cited by 1
- ONote.repr_opow_aux₁proof · cited by 1
- Ordinal.lt_add_iff_of_isSuccLimitproof · cited by 1
- Ordinal.isNormal_veblenWith_zeroproof · cited by 1
- Ordinal.bounded_singletonproof · cited by 1