theorem Th14:
  (for m holds x.m = y.m) implies x = y
proof
  assume
A1: for m holds x.m = y.m;
  for j be Nat st j in Seg(n+1) holds x.j = y.j
  proof
    let j be Nat;
    assume j in Seg(n+1);
    then reconsider j as Nat of n by Th7;
    x.j = y.j by A1;
    hence thesis;
  end;
  hence thesis by FINSEQ_2:119;
end;
