theorem
  p +* Start-At( k,S) c= s implies IC s =  k
proof
  assume
A1: p +* Start-At( k,S) c= s;
  IC S in dom (p +* Start-At( k,S)) by Th27;
  hence IC s = IC(p +* Start-At( k,S)) by A1,GRFUNC_1:2
    .=  k by Th16;
end;
