theorem
  len p = len q & (for j being Nat st j in dom p holds p.j = q.j) implies p = q
proof
  assume that
A1: len p = len q and
A2: for j being Nat st j in dom p holds p.j = q.j;
  dom p = Seg len p & dom q = Seg len p by A1,FINSEQ_1:def 3;
  hence thesis by A2;
end;
