let s be SCMPDS-State; :: 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: {NAT} = dom (NAT .--> u) by FUNCOP_1:13;
( SCMPDS-OK . NAT = NAT & SCMPDS-OK . mk = INT ) by Th18, Th19, AMI_2:22;
then not mk in dom (NAT .--> u) by A1, NUMBERS:27, TARSKI:def 1;
hence (SCM-Chg (s,u)) . mk = s . mk by FUNCT_4:11; :: thesis: verum