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