reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;

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;
