let I be Program of SCM+FSA ; :: thesis: for n being Element of NAT holds IC SCM+FSA in dom (I +* (Start-At n,SCM+FSA ))
let n be Element of NAT ; :: thesis: IC SCM+FSA in dom (I +* (Start-At n,SCM+FSA ))
dom (Start-At n,SCM+FSA ) = {(IC SCM+FSA )} by FUNCOP_1:19;
then IC SCM+FSA in dom (Start-At n,SCM+FSA ) by TARSKI:def 1;
hence IC SCM+FSA in dom (I +* (Start-At n,SCM+FSA )) by FUNCT_4:13; :: thesis: verum