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;
not i in SCM+FSA-Data*-Loc
by A1, Th12, FUNCT_7:18;
then A3:
i in {NAT } \/ SCM+FSA-Data-Loc
by A2, XBOOLE_0:def 3;
not i in {NAT }
by A1, Th9, Th13, TARSKI:def 1;
hence
i in SCM+FSA-Data-Loc
by A3, XBOOLE_0:def 3; :: thesis: verum