reserve x,y,z, X,Y,Z for set,
  n for Element of NAT;
reserve A for set,
  D for non empty set,
  a,b,c,l,r for Element of D,
  o,o9 for BinOp of D,
  f,g,h for Function of A,D;

theorem Th7:
  o is commutative implies (o,D).:A is commutative
proof
  assume
A1: o is commutative;
  set h = (o,D).:A;
  let f,g be Element of Funcs(A,D);
  thus h.(f,g) = o.:(f, g) by Def2
    .= o.:(g, f) by A1,Th3
    .= h.(g,f) by Def2;
end;
