enrich path with comment: This specification defines a synchronisation assignment, by defining a function SA that gives the position of the synchronisation step. Based on SA, the types FS, BS, SA (and the subtypes OD, ON of SA steps) can be defined.; functions SA : path → nat; comment: a synchronisation assignment assigns for every MPath the position of the synchronisation step; predicates OD : path; comment: the SA step is OD; OD : path × nat; comment: step n is an OD SA step; ON : path × nat; comment: step n is an ON SA step; BS : path × nat; comment: step n is a BS step; FS : path × nat; comment: step n is a BS step; variables pa1, pa2 : path; axioms SA-less : ⊦ MPath(pa) → SA(pa) < # pa; comment: SA is unspecified for non-maximal paths; stepno-consistent : ⊦ MPath(pa) ∧ MPath(pa0) ∧ n ≤ # pa ∧ m ≤ # pa0 ∧ pa[n] = pa0[m] → (SA(pa) < n ↔ SA(pa0) < m); OD-path-def : ⊦ OD(pa) ↔ FPath(pa) ∧ (∀ pa1, pa2. pa1 .first = pa .last ∧ pa2 .first = pa .last ∧ MPath(pa + pa1) ∧ MPath(pa + pa2) → pa1 .last = pa2 .last) ; FS-pathstep-def : ⊦ FS(pa, n) ↔ MPath(pa) ∧ (n < SA(pa) ∨ SA(pa) < n ∧ n < # pa ∧ OD(pa to SA(pa))); used for : ls; BS-pathstep-def : ⊦ BS(pa, n) ↔ MPath(pa) ∧ SA(pa) < n ∧ n < # pa ∧ ¬ OD(pa to SA(pa)); used for : ls; OD-pathstep-def : ⊦ OD(pa, n) ↔ MPath(pa) ∧ n = SA(pa) ∧ OD(pa to SA(pa)); used for : ls; ON-pathstep-def : ⊦ ON(pa, n) ↔ MPath(pa) ∧ n = SA(pa) ∧ ¬ OD(pa to SA(pa)); used for : ls; end enrich