let s be SCM+FSA-State; for t being Element of SCM+FSA-Data*-Loc
for u being FinSequence of INT
for a being Element of SCM+FSA-Data-Loc holds (SCM+FSA-Chg (s,t,u)) . a = s . a
let t be Element of SCM+FSA-Data*-Loc ; for u being FinSequence of INT
for a being Element of SCM+FSA-Data-Loc holds (SCM+FSA-Chg (s,t,u)) . a = s . a
let u be FinSequence of INT ; for a being Element of SCM+FSA-Data-Loc holds (SCM+FSA-Chg (s,t,u)) . a = s . a
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