Theorems · Theorem · order theory
isAtomic_iff_forall_isAtomic_Iic
∀ {α : Type u_2} [inst : PartialOrder α] [inst_1 : OrderBot α], IsAtomic α ↔ ∀ (x : α), IsAtomic ↑(Set.Iic x)- Defined in
- Mathlib.Order.Atoms
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- PartialOrderOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Top.topproof · cited by 9,680
- Set.Elemstatement and proof · cited by 7,166
- PartialOrderstatement and proof · cited by 6,410
- Set.Iicstatement and proof · cited by 1,111
- OrderBotstatement and proof · cited by 1,055
- IsAtomproof · cited by 130
- Subtype.mk_eq_mkproof · cited by 33
- IsAtomicstatement and proof · cited by 20
- IsAtomic.eq_bot_or_exists_atom_leproof · cited by 12
- IsAtom.of_isAtom_coe_Iicproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- isCoatomic_iff_forall_isCoatomic_Iciproof · cited by 0