 reserve x,y,X,Y for set;
reserve G for non empty multMagma,
  D for set,
  a,b,c,r,l for Element of G;
reserve M for non empty multLoopStr;
reserve H for non empty SubStr of G,
  N for non empty MonoidalSubStr of G;

theorem Th50:
  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 11;
end;
