let I be Program of SCM+FSA ; :: thesis: for n being Element of NAT holds (I +* (Start-At n,SCM+FSA )) . (IC SCM+FSA ) = n
let n be Element of NAT ; :: thesis: (I +* (Start-At n,SCM+FSA )) . (IC SCM+FSA ) = n
dom (Start-At n,SCM+FSA ) = {(IC SCM+FSA )} by FUNCOP_1:19;
then A1: IC SCM+FSA in dom (Start-At n,SCM+FSA ) by TARSKI:def 1;
(Start-At n,SCM+FSA ) . (IC SCM+FSA ) = n by FUNCOP_1:87;
hence (I +* (Start-At n,SCM+FSA )) . (IC SCM+FSA ) = n by A1, FUNCT_4:14; :: thesis: verum