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;

theorem
  p is one-to-one & rng p = {x,y,z} & x <> y & y <> z & x <> z implies
  len p = 3
proof
  assume that
A1: p is one-to-one and
A2: rng p = {x,y,z} and
A3: x <> y and
A4: y <> z and
A5: x <> z;
  <* x,y,z *> is one-to-one by A3,A4,A5,Th93;
  hence thesis by A1,A2,Th98;
end;
