Theorems · Theorem · order theory
isSimpleOrder_iff_isAtom_top
∀ {α : Type u_2} [inst : PartialOrder α] [inst_1 : BoundedOrder α], IsSimpleOrder α ↔ IsAtom ⊤- Defined in
- Mathlib.Order.Atoms
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 14 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- le_topproof · cited by 411
- BoundedOrderstatement and proof · cited by 270
- IsAtomstatement and proof · cited by 130
- eq_or_lt_of_leproof · cited by 92
- IsSimpleOrderstatement and proof · cited by 54
- isAtom_topproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- OrderIso.isSimpleOrder_iffproof · cited by 12
- Set.isSimpleOrder_Iic_iff_isAtomproof · cited by 3
- isSimpleOrder_iff_isCoatom_botproof · cited by 2