
theorem Th5:
  for p, q being non empty FinSequence st p.1 = q.1 holds 1 <= len
  maxPrefix(p,q)
proof
  let p, q be non empty FinSequence such that
A1: p.1 = q.1 and
A2: 1 > len maxPrefix(p,q);
A3: <*p.1*> c= p by Th4;
  <*p.1*> c= q by A1,Th4;
  then <*p.1*> c= maxPrefix(p,q) by A3,Def1;
  then len <*p.1*> <= len maxPrefix(p,q) by FINSEQ_1:63;
  hence contradiction by A2,FINSEQ_1:39;
end;
