let G be non empty 1-sorted ; :: thesis: for s being SCM-State of G

for u being natural Number

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 natural Number

for mk being Element of SCM-Data-Loc holds (SCM-Chg (s,u)) . mk = s . mk

let u be natural Number ; :: 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

NAT in SCM-Memory by AMI_2:22;

then ( SCM-OK . NAT = 0 & SCM-OK . mk = 1 ) by AMI_2:def 4;

then not mk in dom (NAT .--> u) by TARSKI:def 1;

hence (SCM-Chg (s,u)) . mk = s . mk by FUNCT_4:11; :: thesis: verum

for u being natural Number

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 natural Number

for mk being Element of SCM-Data-Loc holds (SCM-Chg (s,u)) . mk = s . mk

let u be natural Number ; :: 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

NAT in SCM-Memory by AMI_2:22;

then ( SCM-OK . NAT = 0 & SCM-OK . mk = 1 ) by AMI_2:def 4;

then not mk in dom (NAT .--> u) by TARSKI:def 1;

hence (SCM-Chg (s,u)) . mk = s . mk by FUNCT_4:11; :: thesis: verum