Theorems · Theorem · order theory
isSimpleOrder_iff_isCoatom_bot
∀ {α : Type u_2} [inst : PartialOrder α] [inst_1 : BoundedOrder α], IsSimpleOrder α ↔ IsCoatom ⊥- Defined in
- Mathlib.Order.Atoms
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderBoundedOrder
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
- BoundedOrderstatement and proof · cited by 270
- IsCoatomstatement · cited by 114
- IsSimpleOrderstatement · cited by 54
- isSimpleOrder_iff_isAtom_topproof · cited by 3
- isSimpleOrder_iff_isSimpleOrder_orderDualproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Set.isSimpleOrder_Ici_iff_isCoatomproof · cited by 4
- AddAction.isCoatom_stabilizer_iff_preprimitiveproof · cited by 1