reserve i,j,k,n,m for Nat,
  x,y,z,y1,y2 for object, X,Y,D for set,
  p,q for XFinSequence;
reserve k1,k2 for Nat;
reserve D for non empty set,
  F,G for XFinSequence of D,
  b for BinOp of D,
  d,d1,d2 for Element of D;
reserve F for XFinSequence,
        rF,rF1,rF2 for real-valued XFinSequence,
        r for Real,
        cF,cF1,cF2 for complex-valued XFinSequence,
        c,c1,c2 for Complex;
reserve r,s for XFinSequence;

theorem
  for D being set, F,G be XFinSequence of D^omega holds
    F c= G implies FlattenSeq F c= FlattenSeq G
proof
  let D be set, F,G be XFinSequence of D^omega;
  assume F c= G;
  then consider F9 being XFinSequence of D^omega such that
A1: F ^ F9 = G by Th79;
  FlattenSeq F ^ FlattenSeq F9 = FlattenSeq G by A1,Th74;
  hence thesis by AFINSQ_1:74;
end;
