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

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