Proposition 6

For every finite set E which is totally ordered and has n elements $(n \geqslant 1)$, there exists a unique isomorphism of E onto the interval $[1, n]$.

Since E and $[1, n]$ are well-ordered (§ 4, no. 4, Proposition 3, Corollary 1) and have the same number of elements (Proposition 5), the result follows from Theorem 3 of § 2, no. 5 and Corollary 2 to Proposition 2 of § 4, no. 2.