reserve p,q,r for FinSequence;
reserve u,v,x,y,y1,y2,z for object, A,D,X,Y for set;
reserve i,j,k,l,m,n for Nat;
reserve J for Nat;

theorem
  for p,q being FinSequence st p c= q holds q|len p = p
proof
  let p,q be FinSequence such that
A1: p c= q;
A2: for k being Nat st k in dom p holds p.k = (q|len p).k
  proof
    let k be Nat;
    assume
A3: k in dom p;
    then
A4: k <= len p by Th25;
    thus p.k = q.k by A1,A3,GRFUNC_1:2
      .= (q|len p).k by A4,Th110;
  end;
  len p <= len q by A1,FINSEQ_1:63;
  then len(q|len p) = len p by FINSEQ_1:59;
  then dom(q|len p) = dom p by Th27;
  hence thesis by A2;
end;
