theorem Th49:
  [* i,1_(H.i) *] = 1_FreeProduct(H)
proof
  [i,1_(H.i)] in FreeAtoms(H) by Th9;
  then <*[i,1_(H.i)]*> is FinSequence of FreeAtoms(H) by FINSEQ_1:74;
  then <*[i,1_(H.i)]*> in FreeAtoms(H)* by FINSEQ_1:def 11;
  then A1: <*[i,1_(H.i)]*> in the carrier of FreeAtoms(H)*+^+<0>
    by MONOID_0:61;
  A2: [<*[i,1_(H.i)]*>,{}] in ReductionRel(H) by Th29;
  ReductionRel(H) c= EqCl ReductionRel(H) by MSUALG_5:def 1;
  then Class(EqCl ReductionRel H,{}) = [*i,1_(H.i)*] by A1, A2, EQREL_1:35;
  hence thesis by Th45;
end;
