let s be SCM-State; :: thesis: for t being Element of SCM-Data-Loc

for u being Integer holds (SCM-Chg (s,t,u)) . NAT = s . NAT

let t be Element of SCM-Data-Loc ; :: thesis: for u being Integer holds (SCM-Chg (s,t,u)) . NAT = s . NAT

let u be Integer; :: thesis: (SCM-Chg (s,t,u)) . NAT = s . NAT

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

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

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

for u being Integer holds (SCM-Chg (s,t,u)) . NAT = s . NAT

let t be Element of SCM-Data-Loc ; :: thesis: for u being Integer holds (SCM-Chg (s,t,u)) . NAT = s . NAT

let u be Integer; :: thesis: (SCM-Chg (s,t,u)) . NAT = s . NAT

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

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

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