reserve p, q, x, y for Real,
  n for Nat;
reserve X for non empty TopSpace,
  a, b, c, d, e, f for Point of X,
  T for non empty pathwise_connected TopSpace,
  a1, b1, c1, d1, e1, f1 for Point of T;
reserve x0, x1 for Point of X,
  P, Q for Path of x0,x1,
  y0, y1 for Point of T,
  R, V for Path of y0,y1;

theorem
  for S being non empty TopSpace, s being Point of S for x, y being
Element of pi_1(S,s) for P, Q being Loop of s st x = Class(EqRel(S,s),P) & y =
  Class(EqRel(S,s),Q) holds x*y = Class(EqRel(S,s),P+Q) by Lm4;
