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
  sqrreal is_distributive_wrt multreal
proof
  let x1,x2 be Element of REAL;
  thus sqrreal.(multreal.(x1,x2)) = sqrreal.(x1*x2) by BINOP_2:def 11
    .= (x1*x2)^2 by Def2
    .= x1^2*x2^2
    .= multreal.(x1^2,x2^2) by BINOP_2:def 11
    .= multreal.(sqrreal.x1,x2^2) by Def2
    .= multreal.(sqrreal.x1,sqrreal.x2) by Def2;
end;
