 reserve x for object;
 reserve G for non empty 1-sorted;
 reserve A for Subset of G;
 reserve y,y1,y2,Y,Z for set;
 reserve k for Nat;
 reserve G for Group;
 reserve a,g,h for Element of G;
 reserve A for Subset of G;
reserve G for non empty multMagma,
  A,B,C for Subset of G;
reserve a,b,g,g1,g2,h,h1,h2 for Element of G;

theorem Th34:
  G is associative implies A * g * h = A * (g * h)
proof
  assume G is associative;
  hence A * g * h = A * ({g} * {h}) by Th10
    .= A * (g * h) by Th18;
end;
