let I be Program of SCMPDS ; :: thesis: (Initialized I) | NAT = I

A1: now

assume IC SCMPDS in NAT ; :: thesis: contradiction
then reconsider l = IC SCMPDS as Instruction-Location of SCMPDS by AMI_1:def 4;
l = IC SCMPDS ;
hence contradiction by AMI_1:48; :: thesis: verum

end;

( dom I c= NAT & dom (Start-At (inspos 0 )) = {(IC SCMPDS )} ) by FUNCOP_1:19, RELAT_1:def 18;
hence (Initialized I) | NAT = I by A1, FUNCT_4:82, ZFMISC_1:56; :: thesis: verum