reserve x,y,z for object, X for set, I for non empty set, i,j for Element of I,
    M0 for multMagma-yielding Function,
    M for non empty multMagma-yielding Function,
    M1, M2, M3 for non empty multMagma,
    G for Group-like multMagma-Family of I,
    H for Group-like associative multMagma-Family of I;
reserve p, q for FinSequence of FreeAtoms(H), g,h for Element of H.i,
  k for Nat;
reserve s,t for Element of FreeProduct(H);

theorem Th63:
  len nf s = 0 implies s = 1_FreeProduct(H)
proof
  assume len nf s = 0;
  then nf s = {};
  then A1: {} in s by Def7;
  consider x being Element of FreeAtoms(H)*+^+<0> such that
    A2: s = Class(EqCl ReductionRel H,x) by EQREL_1:36;
  thus s = Class(EqCl ReductionRel H,{}) by A1, A2, EQREL_1:23
    .= 1_FreeProduct(H) by Th45;
end;
