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
for v being Element of NAT holds (SCM-Chg s,t,u) . v = s . v
let s be SCM-State of G; :: thesis: for t being Element of SCM-Data-Loc
for u being Element of G
for v being Element of NAT holds (SCM-Chg s,t,u) . v = s . v
let t be Element of SCM-Data-Loc ; :: thesis: for u being Element of G
for v being Element of NAT holds (SCM-Chg s,t,u) . v = s . v
let u be Element of G; :: thesis: for v being Element of NAT holds (SCM-Chg s,t,u) . v = s . v
let v be Element of NAT ; :: thesis: (SCM-Chg s,t,u) . v = s . v
A1: ( SCM-Instr G <> the carrier of G & {t} = dom (t .--> u) ) by Def2, FUNCOP_1:19;
( (SCM-OK G) . v = SCM-Instr G & (SCM-OK G) . t = the carrier of G ) by Th3, Th4;
then not v in dom (t .--> u) by A1, TARSKI:def 1;
hence (SCM-Chg s,t,u) . v = s . v by FUNCT_4:12; :: thesis: verum