reserve i,j,k,n for Nat;
reserve D for non empty set,
  p for Element of D,
  f,g for FinSequence of D;

theorem
  for f being FinSequence holds
  for i1,i2 be Nat st i1<=i2 holds (f|i1)|i2=f|i1 & (f|i2)|i1=f|i1
proof
  let f be FinSequence;
  let i1,i2 be Nat;
  assume
A1: i1<=i2;
  len (f|i1)<=i1 by Th17;
  hence (f|i1)|i2=f|i1 by A1,FINSEQ_1:58,XXREAL_0:2;
  Seg i1 c= Seg i2 by A1,FINSEQ_1:5;
  hence thesis by FUNCT_1:51;
end;
