Theorems · Theorem · order theory
IsCompl.isCoatom_iff_isAtom
∀ {α : Type u_2} [inst : Lattice α] [inst_1 : BoundedOrder α] [IsModularLattice α] {a b : α},
IsCompl a b → (IsCoatom a ↔ IsAtom b)- Defined in
- Mathlib.Order.Atoms
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Latticestatement and proof · cited by 916
- IsComplstatement and proof · cited by 351
- BoundedOrderstatement and proof · cited by 270
- IsAtomstatement · cited by 130
- IsCoatomstatement · cited by 114
- IsModularLatticestatement and proof · cited by 86
- IsCompl.symmproof · cited by 80
- IsCompl.isAtom_iff_isCoatomproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- isCoatom_complproof · cited by 2
- Set.isCoatom_iffproof · cited by 1