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