theorem
 for p,q being PartState of S, k being Nat st IC S in dom q
  holds IncIC(p+*q,k) = p +* IncIC(q,k)
proof let p,q be PartState of S, k be Nat;
  assume IC S in dom q;
   then IC(p+*q) = IC q by FUNCT_4:13;
 hence IncIC(p+*q,k) = p +* IncIC(q,k) by FUNCT_4:14;
end;
