let s be SCMPDS-State; :: thesis: for t being Element of SCM-Data-Loc
for u being Integer
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 Integer
for v being Element of NAT holds (SCM-Chg s,t,u) . v = s . v
let u be Integer; :: 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: {t} = dom (t .--> u) by FUNCOP_1:19;
( SCMPDS-OK . v = SCMPDS-Instr & SCMPDS-OK . t = INT ) by Th19, Th20;
then not v in dom (t .--> u) by A1, Th17, TARSKI:def 1;
hence (SCM-Chg s,t,u) . v = s . v by FUNCT_4:12; :: thesis: verum