let G be non empty good 1-sorted ; :: thesis: for s being SCM-State of G
for t being Element of SCM-Data-Loc
for u being Element of G holds (SCM-Chg (s,t,u)) . NAT = s . NAT
let s be SCM-State of G; :: thesis: for t being Element of SCM-Data-Loc
for u being Element of G holds (SCM-Chg (s,t,u)) . NAT = s . NAT
let t be Element of SCM-Data-Loc ; :: thesis: for u being Element of G holds (SCM-Chg (s,t,u)) . NAT = s . NAT
let u be Element of G; :: thesis: (SCM-Chg (s,t,u)) . NAT = s . NAT
A1: ( NAT <> the carrier of G & {t} = dom (t .--> u) ) by Def2, FUNCOP_1:13;
( (SCM-OK G) . NAT = NAT & (SCM-OK G) . t = the carrier of G ) by Th2, Th3, AMI_2:22;
then not NAT in dom (t .--> u) by A1, TARSKI:def 1;
hence (SCM-Chg (s,t,u)) . NAT = s . NAT by FUNCT_4:11; :: thesis: verum