let I, J, K be Program of SCM+FSA ; :: thesis: (I ';' J) ';' K = I ';' (J ';' K)
XX: ProgramPart (Relocated (J ';' K),(card I)) =
(ProgramPart (Relocated (Directed J),(card I))) +* (ProgramPart (Relocated [(ProgramPart (Relocated K,(card J)))],(card I)))
by Th21
.=
(ProgramPart (Relocated (Directed J),(card I))) +* (ProgramPart (Relocated K,((card J) + (card I))))
by Th22
;
thus (I ';' J) ';' K =
(I ';' (Directed J)) +* (ProgramPart (Relocated K,(card (I ';' J))))
by Th52
.=
(Directed I) +* ((ProgramPart (Relocated (Directed J),(card I))) +* (ProgramPart (Relocated K,(card (I ';' J)))))
by FUNCT_4:15
.=
I ';' (J ';' K)
by XX, Th61
; :: thesis: verum