Every totally ordered set is a distributive lattice.
A totally ordered set means, for every two elements of the set $a$ and $b$, either $a \leq b$ or $b \leq a$, and thus $a \leq b$ if and only if $a \wedge b = a$ (meet operation) and $a \vee b = b$ (join operation).
A lattice $(L,∨,∧)$ is distributive if the following identity holds for all $x, y,$ and $z$ in $L$:
$$x ∧ (y ∨ z) = (x ∧ y) ∨ (x ∧ z)$$.
$\text{LHS} = x \wedge (y \vee z)$.
For a totally ordered set, this will return $x$, iff order of $x$ is $\leq$ either $y$ or $z$. Otherwise it will return the larger of $y$ and $z$.
The same thing is applicable for $\text{RHS}$ also making $\text{LHS} = \text{RHS}$ for a totally ordered set.
