Theorems · Theorem · order theory
Order.pred_lt_iff_ne_bot
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : PredOrder α] {a : α} [inst_2 : OrderBot α], Order.pred a < a ↔ a ≠ ⊥- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
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.
- PartialOrderstatement and proof · cited by 6,410
- Bot.botstatement · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- PredOrderstatement and proof · cited by 334
- Order.predstatement · cited by 273
- Order.pred_lt_iff_not_isMinproof · cited by 4
- not_isMin_iff_ne_botproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Order.pred_eq_sSupproof · cited by 1