let I be Program of SCM+FSA ; :: thesis: for f being FinSeq-Location
for l being Element of NAT holds not f in dom (I +* (Start-At l,SCM+FSA ))
let f be FinSeq-Location ; :: thesis: for l being Element of NAT holds not f in dom (I +* (Start-At l,SCM+FSA ))
let l be Element of NAT ; :: thesis: not f in dom (I +* (Start-At l,SCM+FSA ))
assume f in dom (I +* (Start-At l,SCM+FSA )) ; :: thesis: contradiction
then f in (dom I) \/ (dom (Start-At l,SCM+FSA )) by FUNCT_4:def 1;
then A1: ( f in dom I or f in dom (Start-At l,SCM+FSA ) ) by XBOOLE_0:def 3;
( dom I c= NAT & f in FinSeq-Locations ) by RELAT_1:def 18, SCMFSA_2:10;
hence contradiction by A1, Th10, SCMFSA_2:14, XBOOLE_0:3; :: thesis: verum