Theorems · Theorem · order theory
isCoatomic_of_isAtomic_of_complementedLattice_of_isModular
∀ {α : Type u_2} [inst : Lattice α] [inst_1 : BoundedOrder α] [IsModularLattice α] [ComplementedLattice α] [IsAtomic α],
IsCoatomic α- 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.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Set.Elemproof · cited by 7,166
- Bot.botproof · cited by 4,720
- Set.Iciproof · cited by 1,070
- Latticestatement and proof · cited by 916
- IsComplproof · cited by 351
- BoundedOrderstatement and proof · cited by 270
- IsAtomproof · cited by 130
- IsModularLatticestatement and proof · cited by 86
- IsCompl.symmproof · cited by 80
- ComplementedLatticestatement and proof · cited by 30
- IsCoatomicstatement · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- isAtomic_of_isCoatomic_of_complementedLattice_of_isModularproof · cited by 1
- isAtomic_iff_isCoatomicproof · cited by 0