theorem Th45:
  for I being set, H being Group-like associative multMagma-Family of I
  holds 1_FreeProduct(H) = Class(EqCl ReductionRel H,{})
proof
  let I be set, H be Group-like associative multMagma-Family of I;
  thus 1_FreeProduct(H)
     = Class(EqCl ReductionRel H,1_(FreeAtoms(H)*+^+<0>)) by ALGSTR_4:49
    .= Class(EqCl ReductionRel H,{}) by MONOID_0:61;
end;
