|- !P s. s IN TRACES P ==> (ALPHA (P / s) = ALPHA P) /\ (TRACES (P / s) = {t | APPEND s t IN TRACES P})
|- !P s. s IN TRACES P ==> IS_PROCESS (ALPHA P,{t | APPEND s t IN TRACES P})
|- !P s. s IN TRACES P ==> (ALPHA (P / s) = ALPHA P)
|- !P s. s IN TRACES P ==> (TRACES (P / s) = {t | APPEND s t IN TRACES P})