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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.

  • Setstatement · cited by 53,352
  • Set.Elemstatement and proof · cited by 7,166
  • Set.Ioostatement and proof · cited by 1,214
  • Latticestatement and proof · cited by 916
  • OrderIsostatement · cited by 874
  • IsModularLatticestatement and proof · cited by 86

Cited by5

Results whose statement or proof uses this declaration.