Theorems · Theorem · order theory
IsSimpleOrder.eq_bot_of_lt
∀ {α : Type u_2} [inst : Preorder α] [inst_1 : BoundedOrder α] [IsSimpleOrder α] {a b : α}, a < b → a = ⊥- Defined in
- Mathlib.Order.Atoms
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
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.
- Preorderstatement and proof · cited by 7,952
- Bot.botstatement · cited by 4,720
- BoundedOrderstatement and proof · cited by 270
- IsSimpleOrderstatement and proof · cited by 54
- LT.lt.ne_topproof · cited by 34
- IsSimpleOrder.eq_bot_or_eq_topproof · cited by 32
Cited by2
Results whose statement or proof uses this declaration.
- IsSimpleOrder.lt_top_iff_eq_botproof · cited by 0
- LT.lt.eq_botproof · cited by 0