let i be Element of SCM+FSA-Memory ; :: thesis: ( SCM+FSA-OK . i = INT * implies i in SCM+FSA-Data*-Loc )
assume A1: SCM+FSA-OK . i = INT * ; :: thesis: i in SCM+FSA-Data*-Loc
not i in NAT by A1, Th11, Th13;
then A2: i in ({NAT } \/ SCM+FSA-Data-Loc ) \/ SCM+FSA-Data*-Loc by Th8, XBOOLE_0:def 3;

now

assume A3: i in {NAT } \/ SCM+FSA-Data-Loc ; :: thesis: contradiction
not i in {NAT } by A1, Th9, Th13, TARSKI:def 1;
then i in SCM+FSA-Data-Loc by A3, XBOOLE_0:def 3;
hence contradiction by A1, Th10, FUNCT_7:18; :: thesis: verum

end;

hence i in SCM+FSA-Data*-Loc by A2, XBOOLE_0:def 3; :: thesis: verum