20.4 Precedes relation on composite operations

Definition:

Let M1,M2 be composite operations. We write M1 → M2 if

O1 ∈ Ψ(M1), O2 ∈ Ψ(M2) ⇒ O1 → O2

Definition:

Let M1,M2 be composite operations. We write M1 || M2 if

O1 ∈ Ψ(M1), O2 ∈ Ψ(M2) ⇒ O1 || O2

Note that it is possible to have ¬(M1 → M2) ∧ ¬(M2 → M1) ∧ ¬(M1 || M2)