let s be SCM+FSA-State; :: thesis: for t being Element of SCM+FSA-Data-Loc
for u being Integer holds (SCM+FSA-Chg (s,t,u)) . NAT = s . NAT
let t be Element of SCM+FSA-Data-Loc ; :: thesis: for u being Integer holds (SCM+FSA-Chg (s,t,u)) . NAT = s . NAT
let u be Integer; :: thesis: (SCM+FSA-Chg (s,t,u)) . NAT = s . NAT
( SCM+FSA-OK . t = INT & {t} = dom (t .--> u) ) by Th10, FUNCOP_1:13;
then not NAT in dom (t .--> u) by Th9, NUMBERS:27, TARSKI:def 1;
hence (SCM+FSA-Chg (s,t,u)) . NAT = s . NAT by FUNCT_4:11; :: thesis: verum