let s be SCM-State; :: thesis: for u being natural Number

for mk being Element of SCM-Data-Loc holds (SCM-Chg (s,u)) . mk = s . mk

let u be natural Number ; :: thesis: for mk being Element of SCM-Data-Loc holds (SCM-Chg (s,u)) . mk = s . mk

let mk be Element of SCM-Data-Loc ; :: thesis: (SCM-Chg (s,u)) . mk = s . mk

( (SCM-VAL * SCM-OK) . NAT = NAT & (SCM-VAL * SCM-OK) . mk = INT ) by Th1, Th2;

then not mk in dom (NAT .--> u) by NUMBERS:7, TARSKI:def 1;

hence (SCM-Chg (s,u)) . mk = s . mk by FUNCT_4:11; :: thesis: verum

for mk being Element of SCM-Data-Loc holds (SCM-Chg (s,u)) . mk = s . mk

let u be natural Number ; :: thesis: for mk being Element of SCM-Data-Loc holds (SCM-Chg (s,u)) . mk = s . mk

let mk be Element of SCM-Data-Loc ; :: thesis: (SCM-Chg (s,u)) . mk = s . mk

( (SCM-VAL * SCM-OK) . NAT = NAT & (SCM-VAL * SCM-OK) . mk = INT ) by Th1, Th2;

then not mk in dom (NAT .--> u) by NUMBERS:7, TARSKI:def 1;

hence (SCM-Chg (s,u)) . mk = s . mk by FUNCT_4:11; :: thesis: verum