let I be Program of SCM+FSA; :: thesis: for f being FinSeq-Location holds not f in dom I
let f be FinSeq-Location ; :: thesis: not f in dom I
A1: dom I c= NAT by RELAT_1:def 18;
assume f in dom I ; :: thesis: contradiction
then reconsider f = f as Element of NAT by A1;
f = f ;
hence contradiction by SCMFSA_2:60; :: thesis: verum