Order and Arithmetic of ℝ on Classes, Continued

This helper adopts the setting of The Real Numbers, with the Natural Numbers, Integers and Rationals Identified with Subsets of the Reals, and Completeness: $\mathbb{R}$, its order $\le$, its operation $+$ and its elements $0$ and $1$ are as in The Real Numbers, with the Natural Numbers, Integers and Rationals Identified with Subsets of the Reals, and Completeness (ii); $<$ is the strict relation associated with $\le$, and for $x,y\in\mathbb{R}$, $x-y$ is the difference of $x$ and $y$. Let $x$ and $y$ be real numbers.

(i) $1\le 1+1$.

(ii) If $x-y=0$, then $x=y$.