Theorems · Theorem · order theory
Order.lt_succ_iff
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : SuccOrder α] {a b : α} [NoMaxOrder α], a < Order.succ b ↔ a ≤ b- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- LinearOrderstatement and proof · cited by 8,572
- Order.succstatement · cited by 633
- SuccOrderstatement and proof · cited by 574
- NoMaxOrderstatement and proof · cited by 340
- not_isMaxproof · cited by 46
- Order.lt_succ_iff_of_not_isMaxproof · cited by 17
Cited by22
Results whose statement or proof uses this declaration.
- Ordinal.div_leproof · cited by 6
- Ordinal.lt_mul_succ_divproof · cited by 5
- Ordinal.lt_opow_succ_log_selfproof · cited by 5
- Cardinal.card_le_iffproof · cited by 4
- Cardinal.lift_succproof · cited by 4
- Cardinal.lt_aleph_one_iffproof · cited by 3
- Ordinal.type_lt_mem_range_succ_iffproof · cited by 3
- Ordinal.lsub_le_succ_iSupproof · cited by 2
- Order.lt_succ_iff_eq_or_ltproof · cited by 2
- Ordinal.mul_add_div_mulproof · cited by 2
- Order.lt_succ_bot_iffproof · cited by 1
- Ordinal.blsub_le_bsup_succproof · cited by 1