Theorems · Definition · order theory
IsCompl.IicOrderIsoIci
{α : Type u_1} →
[inst : Lattice α] →
[inst_1 : BoundedOrder α] → [IsModularLattice α] → {a b : α} → IsCompl a b → ↑(Set.Iic a) ≃o ↑(Set.Ici b)The diamond isomorphism between the intervals Set.Iic a and Set.Ici b.
- Defined in
- Mathlib.Order.ModularLattice
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.Elemstatement · cited by 7,166
- Set.Iccproof · cited by 1,702
- Set.Iicstatement and proof · cited by 1,111
- Set.Icistatement and proof · cited by 1,070
- Latticestatement and proof · cited by 916
- OrderIsostatement · cited by 874
- IsComplstatement and proof · cited by 351
- BoundedOrderstatement and proof · cited by 270
- IsModularLatticestatement and proof · cited by 86
- OrderIso.transproof · cited by 31
- OrderIso.setCongrproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- IsCompl.isAtom_iff_isCoatomproof · cited by 3
- isCoatomic_of_isAtomic_of_complementedLattice_of_isModularproof · cited by 2