let s be SCM-State; :: thesis: for t being Element of SCM-Data-Loc
for u being Integer
for mk being Element of SCM-Data-Loc st mk <> t holds
(SCM-Chg s,t,u) . mk = s . mk
let t be Element of SCM-Data-Loc ; :: thesis: for u being Integer
for mk being Element of SCM-Data-Loc st mk <> t holds
(SCM-Chg s,t,u) . mk = s . mk
let u be Integer; :: thesis: for mk being Element of SCM-Data-Loc st mk <> t holds
(SCM-Chg s,t,u) . mk = s . mk
let mk be Element of SCM-Data-Loc ; :: thesis: ( mk <> t implies (SCM-Chg s,t,u) . mk = s . mk )
assume A1: mk <> t ; :: thesis: (SCM-Chg s,t,u) . mk = s . mk
{t} = dom (t .--> u) by FUNCOP_1:19;
then not mk in dom (t .--> u) by A1, TARSKI:def 1;
hence (SCM-Chg s,t,u) . mk = s . mk by FUNCT_4:12; :: thesis: verum