let s be SCM+FSA-State; :: thesis: for t being Element of SCM+FSA-Data*-Loc

for u being FinSequence of INT

for mk being Element of SCM+FSA-Data*-Loc st mk <> t holds

(SCM+FSA-Chg (s,t,u)) . mk = s . mk

let t be Element of SCM+FSA-Data*-Loc ; :: thesis: for u being FinSequence of INT

for mk being Element of SCM+FSA-Data*-Loc st mk <> t holds

(SCM+FSA-Chg (s,t,u)) . mk = s . mk

let u be FinSequence of INT ; :: thesis: for mk being Element of SCM+FSA-Data*-Loc st mk <> t holds

(SCM+FSA-Chg (s,t,u)) . mk = s . mk

let mk be Element of SCM+FSA-Data*-Loc ; :: thesis: ( mk <> t implies (SCM+FSA-Chg (s,t,u)) . mk = s . mk )

assume A1: mk <> t ; :: thesis: (SCM+FSA-Chg (s,t,u)) . mk = s . mk

not mk in dom (t .--> u) by A1, TARSKI:def 1;

hence (SCM+FSA-Chg (s,t,u)) . mk = s . mk by FUNCT_4:11; :: thesis: verum

for u being FinSequence of INT

for mk being Element of SCM+FSA-Data*-Loc st mk <> t holds

(SCM+FSA-Chg (s,t,u)) . mk = s . mk

let t be Element of SCM+FSA-Data*-Loc ; :: thesis: for u being FinSequence of INT

for mk being Element of SCM+FSA-Data*-Loc st mk <> t holds

(SCM+FSA-Chg (s,t,u)) . mk = s . mk

let u be FinSequence of INT ; :: thesis: for mk being Element of SCM+FSA-Data*-Loc st mk <> t holds

(SCM+FSA-Chg (s,t,u)) . mk = s . mk

let mk be Element of SCM+FSA-Data*-Loc ; :: thesis: ( mk <> t implies (SCM+FSA-Chg (s,t,u)) . mk = s . mk )

assume A1: mk <> t ; :: thesis: (SCM+FSA-Chg (s,t,u)) . mk = s . mk

not mk in dom (t .--> u) by A1, TARSKI:def 1;

hence (SCM+FSA-Chg (s,t,u)) . mk = s . mk by FUNCT_4:11; :: thesis: verum