reserve s for set,
  i,j for natural Number,
  k for Nat,
  x,x1,x2,x3 for Real,
  r,r1,r2,r3,r4 for Real,
  F,F1,F2,F3 for real-valued FinSequence,
  R,R1,R2 for Element of i-tuples_on REAL;
reserve z,z1,z2 for Element of COMPLEX;

theorem
  Product ((i+j) |->z) = (Product (i|->z))*(Product (j|->z))
proof
  reconsider i,j as Nat by TARSKI:1;
  Product ((i+j) |->z) = multcomplex.(multcomplex$$(i|->z),multcomplex$$(j
  |->z)) by SETWOP_2:26
    .= (Product (i|->z))*(Product (j|->z)) by BINOP_2:def 5;
  hence thesis;
end;
