Theorems · Theorem · order theory
Order.le_succ_bot_iff
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : SuccOrder α] {a : α} [inst_2 : OrderBot α],
a ≤ Order.succ ⊥ ↔ a = ⊥ ∨ a = Order.succ ⊥- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderSuccOrderOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Bot.botstatement and proof · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- Order.succstatement and proof · cited by 633
- SuccOrderstatement and proof · cited by 574
- le_bot_iffproof · cited by 116
- Order.le_succ_iff_eq_or_leproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Cardinal.le_one_iffproof · cited by 1