let s be SCM+FSA-State; :: thesis: 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 ; :: thesis: 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 ; :: thesis: 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 ; :: thesis: (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; :: thesis: verum

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 ; :: thesis: 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 ; :: thesis: 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 ; :: thesis: (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; :: thesis: verum