theorem
 for p,q being PartState of S, k being Nat st IC S in dom q
  holds DecIC(p+*IncIC(q,k),k) = p +* q
proof let p,q be PartState of S, k being Nat such that
A1: IC S in dom q;
  IC S in dom IncIC(q,k) by Th52;
 hence DecIC(p+*IncIC(q,k),k) = p +* DecIC(IncIC(q,k),k) by Th72
      .= p +* q by A1,Th73;
end;
