Theorems · Theorem · order theory
ComplementedLattice.isStronglyAtomic
∀ {α : Type u_2} [inst : Lattice α] [inst_1 : BoundedOrder α] [IsModularLattice α] [ComplementedLattice α] [IsAtomic α],
IsStronglyAtomic αA complemented modular atomic lattice is strongly atomic. Not an instance to prevent loops.
- Defined in
- Mathlib.Order.Atoms
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.Elemproof · cited by 7,166
- Bot.botproof · cited by 4,720
- LE.le.transproof · cited by 3,151
- LT.lt.leproof · cited by 2,189
- Set.Iicproof · cited by 1,111
- Latticestatement and proof · cited by 916
- LT.lt.neproof · cited by 872
- IsComplproof · cited by 351
- CovByproof · cited by 290
- BoundedOrderstatement and proof · cited by 270
- Codisjointproof · cited by 197
- sup_leproof · cited by 159
Cited by2
Results whose statement or proof uses this declaration.
- ComplementedLattice.isStronglyCoatomicproof · cited by 1
- ComplementedLattice.isStronglyCoatomic'proof · cited by 0