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;

theorem
  Product ((i*j) |->r) = Product (j |-> (Product (i|->r)))
proof
  reconsider r as Element of REAL by XREAL_0:def 1;
  reconsider pr = Product (i|->r) as Element of REAL;
  i is Nat & j is Nat by TARSKI:1;
  then Product ((i*j) |->r) = Product (j |-> pr) by SETWOP_2:27;
  hence thesis;
end;
