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
for mk being Element of SCM-Data-Loc st mk <> t holds
(SCM-Chg (s,t,u)) . mk = s . mk
let s be SCM-State of G; :: thesis: for t being Element of SCM-Data-Loc
for u being Element of G
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 Element of G
for mk being Element of SCM-Data-Loc st mk <> t holds
(SCM-Chg (s,t,u)) . mk = s . mk
let u be Element of G; :: 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
not mk in dom (t .--> u) by A1, TARSKI:def 1;
hence (SCM-Chg (s,t,u)) . mk = s . mk by FUNCT_4:11; :: thesis: verum