For any two elements a,b of a modular lattice, one can consider the intervals [a ∧ b, b] and [a, a ∨ b].
The composition ψφ is an order-preserving map from the interval [a ∧ b, b] to itself which also satisfies the inequality ψ(φ(x)) = (x ∨ a) ∧ b ≥ x.