let G be non empty 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

NAT in SCM-Memory by AMI_2:22;

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

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

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

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

NAT in SCM-Memory by AMI_2:22;

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

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

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