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
A1: {t} = dom (t .--> u) by FUNCOP_1:13;
( (SCM-VAL * SCM-OK) . NAT = NAT & (SCM-VAL * SCM-OK) . t = INT ) by Th1, Th2;
then not NAT in dom (t .--> u) by A1, NUMBERS:7, TARSKI:def 1;
hence (SCM-Chg (s,t,u)) . NAT = s . NAT by FUNCT_4:11; :: thesis: verum