let s be SCM+FSA-State; :: thesis: for t being Element of SCM+FSA-Data*-Loc
for u being FinSequence of INT
for a being Element of SCM+FSA-Data-Loc holds (SCM+FSA-Chg (s,t,u)) . a = s . a
let t be Element of SCM+FSA-Data*-Loc ; :: thesis: for u being FinSequence of INT
for a being Element of SCM+FSA-Data-Loc holds (SCM+FSA-Chg (s,t,u)) . a = s . a
let u be FinSequence of INT ; :: thesis: for a being Element of SCM+FSA-Data-Loc holds (SCM+FSA-Chg (s,t,u)) . a = s . a
let mk be Element of SCM+FSA-Data-Loc ; :: thesis: (SCM+FSA-Chg (s,t,u)) . mk = s . mk
A1: {t} = dom (t .--> u) by FUNCOP_1:13;
( SCM+FSA-OK . t = INT * & SCM+FSA-OK . mk = INT ) by Th10, Th12;
then not mk in dom (t .--> u) by A1, FUNCT_7:16, TARSKI:def 1;
hence (SCM+FSA-Chg (s,t,u)) . mk = s . mk by FUNCT_4:11; :: thesis: verum