theorem Th31:
  for x,y being object st [x,y] in ReductionRel(G)
  holds x is FinSequence of FreeAtoms(G) & y is FinSequence of FreeAtoms(G)
proof
  let x,y be object;
  assume [x,y] in ReductionRel(G);
  then x in field ReductionRel(G) & y in field ReductionRel(G) by RELAT_1:15;
  then x in FreeAtoms(G)* & y in FreeAtoms(G)* by Th30;
  hence thesis by FINSEQ_1:def 11;
end;
