let n be Element of NAT ; :: thesis: for I being Program of SCM+FSA holds (I +* (Start-At (insloc n))) | NAT = I
let I be Program of SCM+FSA ; :: thesis: (I +* (Start-At (insloc n))) | NAT = I
A1: dom I c= NAT by RELAT_1:def 18;
NAT misses dom (Start-At (insloc n))

proof

assume not NAT misses dom (Start-At (insloc n)) ; :: thesis: contradiction
then consider x being set such that
A2: ( x in NAT & x in dom (Start-At (insloc n)) ) by XBOOLE_0:3;
dom (Start-At (insloc n)) = {(IC SCM+FSA )} by FUNCOP_1:19;
hence contradiction by A2, Lm1, TARSKI:def 1; :: thesis: verum

end;

then (I +* (Start-At (insloc n))) | NAT = I | NAT by FUNCT_4:76;
hence (I +* (Start-At (insloc n))) | NAT = I by A1, RELAT_1:97; :: thesis: verum