let s be State of SCM+FSA ; :: thesis: for l being Element of NAT holds DataPart s = DataPart (s +* (Start-At l,SCM+FSA ))
let l be Element of NAT ; :: thesis: DataPart s = DataPart (s +* (Start-At l,SCM+FSA ))

now

let x be set ; :: thesis: ( x in dom (Start-At l,SCM+FSA ) implies not x in Int-Locations \/ FinSeq-Locations )
assume x in dom (Start-At l,SCM+FSA ) ; :: thesis: not x in Int-Locations \/ FinSeq-Locations
then x in {(IC SCM+FSA )} by FUNCOP_1:19;
hence not x in Int-Locations \/ FinSeq-Locations by SCMFSA6A:37, TARSKI:def 1; :: thesis: verum

end;

then dom (Start-At l,SCM+FSA ) misses Int-Locations \/ FinSeq-Locations by XBOOLE_0:3;
hence DataPart s = DataPart (s +* (Start-At l,SCM+FSA )) by FUNCT_4:76, SCMFSA_2:127; :: thesis: verum