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
  len f = len g & (for k st 1 <= k & k <= len f holds f/.k = g/.k)
  implies f = g
proof
  assume that
A1: len f = len g and
A2: for k st 1 <= k & k <= len f holds f/.k = g/.k;
  now
    let k be Nat;
    assume
A3: 1 <= k & k <= len f;
    hence f.k = f/.k by FINSEQ_4:15
      .= g/.k by A2,A3
      .= g.k by A1,A3,FINSEQ_4:15;
  end;
  hence thesis by A1;
end;
