Theorems · Definition · order theory
infIooOrderIsoIooSup
{α : Type u_1} → [inst : Lattice α] → [IsModularLattice α] → (a b : α) → ↑(Set.Ioo (a ⊓ b) a) ≃o ↑(Set.Ioo b (a ⊔ b))The diamond isomorphism between the open intervals (a ⊓ b, a) and (b, a ⊔ b).
- Defined in
- Mathlib.Order.ModularLattice
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LatticeIsModularLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by5
Results whose statement or proof uses this declaration.
- infIooOrderIsoIooSup'proof · cited by 2
- infIooOrderIsoIooSup'_symm_apply_coestatement · cited by 0
- infIooOrderIsoIooSup.congr_simpstatement and proof · cited by 0
- infIooOrderIsoIooSup_symm_apply_coestatement and proof · cited by 0
- infIooOrderIsoIooSup_apply_coestatement and proof · cited by 0