let i be Element of SCM-Memory ; :: thesis: ( SCMPDS-OK . i = INT iff i in SCM-Data-Loc )
thus ( SCMPDS-OK . i = INT implies i in SCM-Data-Loc ) :: thesis: ( i in SCM-Data-Loc implies SCMPDS-OK . i = INT )

proof

assume A1: SCMPDS-OK . i = INT ; :: thesis: i in SCM-Data-Loc
assume A2: not i in SCM-Data-Loc ; :: thesis: contradiction

per cases ( i = NAT or i in NAT ) by A2, Th14;

suppose i = NAT ; :: thesis: contradiction

hence contradiction by A1, Def4, NUMBERS:27; :: thesis: verum

end;

suppose i in NAT ; :: thesis: contradiction

hence contradiction by A1, Def4, Th17; :: thesis: verum

end;

end;

end;

thus ( i in SCM-Data-Loc implies SCMPDS-OK . i = INT ) by Def4; :: thesis: verum