reserve s for set,
  i,j for Nat,
  c,c1,c2,c3 for Complex,
  F,F1,F2 for complex-valued FinSequence,
  R,R1,R2 for i-element complex-valued FinSequence;

theorem
  sqrcomplex is_distributive_wrt multcomplex
proof
  let x1,x2 be Element of COMPLEX;
  thus sqrcomplex.(multcomplex.(x1,x2)) = sqrcomplex.(x1*x2) by BINOP_2:def 5
     .= (x1*x2)^2 by Def1
     .= x1^2*x2^2
     .= multcomplex.(x1^2,x2^2) by BINOP_2:def 5
     .= multcomplex.(sqrcomplex.x1,x2^2) by Def1
     .= multcomplex.(sqrcomplex.x1,sqrcomplex.x2) by Def1;
end;
