Theorems · Theorem · order theory
ComplementedLattice.isStronglyCoatomic
∀ {α : Type u_2} [inst : Lattice α] [inst_1 : BoundedOrder α] [IsModularLattice α] [ComplementedLattice α]
[IsCoatomic α], IsStronglyCoatomic αA complemented modular coatomic lattice is strongly coatomic. Not an instance to prevent loops.
- Defined in
- Mathlib.Order.Atoms
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 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
- IsStronglyCoatomicstatement · cited by 12
- isStronglyAtomic_dual_iff_is_stronglyCoatomicproof · cited by 5
- ComplementedLattice.isStronglyAtomicproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ComplementedLattice.isStronglyAtomic'proof · cited by 0