let s be SCM+FSA-State; :: thesis: for t being Element of SCM+FSA-Data-Loc
for u being Integer
for f being Element of SCM+FSA-Data*-Loc holds (SCM+FSA-Chg s,t,u) . f = s . f
let t be Element of SCM+FSA-Data-Loc ; :: thesis: for u being Integer
for f being Element of SCM+FSA-Data*-Loc holds (SCM+FSA-Chg s,t,u) . f = s . f
let u be Integer; :: thesis: for f being Element of SCM+FSA-Data*-Loc holds (SCM+FSA-Chg s,t,u) . f = s . f
let mk be Element of SCM+FSA-Data*-Loc ; :: thesis: (SCM+FSA-Chg s,t,u) . mk = s . mk
A1: ( SCM+FSA-OK . t = INT & SCM+FSA-OK . mk = INT * ) by Th10, Th12;
{t} = dom (t .--> u) by FUNCOP_1:19;
then not mk in dom (t .--> u) by A1, FUNCT_7:18, TARSKI:def 1;
hence (SCM+FSA-Chg s,t,u) . mk = s . mk by FUNCT_4:12; :: thesis: verum