theorem Th39:
  for N being non empty SubStr of <REAL,+>
  for a,b being Element of N, x,y being Real st
    a = x & b = y holds a*b = x+y
proof
  let N be non empty SubStr of <REAL,+>;
  let a,b be Element of N;
  carr(N) c= carr(<REAL,+>) by Th23;
  then reconsider a9 = a, b9 = b as Element of <REAL,+>;
  a*b = a9*b9 by Th25;
  hence thesis by BINOP_2:def 9;
end;
