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