Theorems · Theorem · order theory
isAtomic_of_isCoatomic_of_complementedLattice_of_isModular
∀ {α : Type u_2} [inst : Lattice α] [inst_1 : BoundedOrder α] [IsModularLattice α] [ComplementedLattice α]
[IsCoatomic α], IsAtomic α- Defined in
- Mathlib.Order.Atoms
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 33 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
- BoundedOrderstatement and proof · cited by 270
- IsModularLatticestatement and proof · cited by 86
- ComplementedLatticestatement and proof · cited by 30
- IsCoatomicstatement and proof · cited by 23
- IsAtomicstatement · cited by 20
- isCoatomic_dual_iff_isAtomicproof · cited by 3
- isCoatomic_of_isAtomic_of_complementedLattice_of_isModularproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- isAtomic_iff_isCoatomicproof · cited by 0