
theorem Th4:
  for p being non empty FinSequence holds <*p.1*> is_a_prefix_of p
proof
  let p be non empty FinSequence;
A1: now
    let x be object;
A2: dom <*p.1*> = Seg 1 by FINSEQ_1:def 8;
    assume x in dom <*p.1*>;
    then x = 1 by A2,FINSEQ_1:2,TARSKI:def 1;
    hence <*p.1*>.x = p.x;
  end;
  len p >= 1 by FINSEQ_1:20;
  then len <*p.1*> <= len p by FINSEQ_1:39;
  then dom <*p.1*> c= dom p by FINSEQ_3:30;
  hence thesis by A1,GRFUNC_1:2;
end;
