|- !P Q. (ALPHA (P PAR Q) = ALPHA P UNION ALPHA Q) /\ (TRACES (P PAR Q) = {s | s IN STAR (ALPHA P UNION ALPHA Q) /\ RESTRICT s (ALPHA P) IN TRACES P /\ RESTRICT s (ALPHA Q) IN TRACES Q})
|- !P Q. IS_PROCESS (ALPHA P UNION ALPHA Q, {s | s IN STAR (ALPHA P UNION ALPHA Q) /\ RESTRICT s (ALPHA P) IN TRACES P /\ RESTRICT s (ALPHA Q) IN TRACES Q})
|- !Q P. ALPHA (P PAR Q) = ALPHA P UNION ALPHA Q
|- !Q P. TRACES (P PAR Q) = {s | s IN STAR (ALPHA P UNION ALPHA Q) /\ RESTRICT s (ALPHA P) IN TRACES P /\ RESTRICT s (ALPHA Q) IN TRACES Q}