$-1$ is the least element of the two's-complement order

In the $\varepsilon$-order with $\varepsilon\equiv\mathrm{true}$ (the extension to $\mathbb{Z}$ of Ho's order $\triangleleft$), $-1$ precedes every other integer:

All two's-complement digits of $-1$ equal $1$, which is the preferred digit at every level.

Formalization Note epsLt ε x y is x ≠ y ∧ (x / 2^k % 2 = 1 ↔ ε k = true) with k = padicValInt 2 (y - x), i.e. $k=\nu_2(y-x)$; integer division is floor division, so x / 2^k % 2 is the $k$-th two's-complement digit of $x$.