let s be SCM+FSA-State; for t being Element of SCM+FSA-Data-Loc
for u being Integer
for f being Element of SCM+FSA-Data*-Loc holds (SCM+FSA-Chg (s,t,u)) . f = s . f
let t be Element of SCM+FSA-Data-Loc ; for u being Integer
for f being Element of SCM+FSA-Data*-Loc holds (SCM+FSA-Chg (s,t,u)) . f = s . f
let u be Integer; for f being Element of SCM+FSA-Data*-Loc holds (SCM+FSA-Chg (s,t,u)) . f = s . f
let mk be Element of SCM+FSA-Data*-Loc ; (SCM+FSA-Chg (s,t,u)) . mk = s . mk
( (SCM*-VAL * SCM+FSA-OK) . t = INT & (SCM*-VAL * SCM+FSA-OK) . mk = INT * )
by Th5, Th6;
then
not mk in dom (t .--> u)
by FUNCT_7:16, TARSKI:def 1;
hence
(SCM+FSA-Chg (s,t,u)) . mk = s . mk
by FUNCT_4:11; verum