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;
