Order of Strictly Positive Real Numbers is Dual of Order of their Reciprocals

Theorem

 * $\forall x, y \in \R: x > y > 0 \implies \dfrac 1 x < \dfrac 1 y$

Proof
From Reciprocal of Strictly Positive Real Number is Strictly Positive:
 * $(1): \quad x > 0 \implies \dfrac 1 x > 0$
 * $(2): \quad y > 0 \implies \dfrac 1 y > 0$

Then: