one_div_pos_of_pos'
plain-language theorem explainer
Establishes that the reciprocal of a positive real number is positive. Analysts working with inequalities or divisions in real analysis would cite it to maintain sign consistency. The proof is a one-line wrapper that rewrites division and applies the standard inverse positivity result.
Claim. For $x$ a real number, if $x > 0$ then $1/x > 0$.
background
The Compat.Mathlib module supplies small alias lemmas and helpers that stabilize names across Mathlib versions and cut duplication. This theorem re-expresses the positivity of the reciprocal using the definition of division as multiplication by the multiplicative inverse.
proof idea
One-line wrapper that applies the inverse positivity lemma after simplifying the division notation.
why it matters
Supplies a stable name for a basic positivity fact, preventing version-specific breakage in the Recognition Science mathematical layer. It supports any downstream argument that divides by positive reals without introducing extra hypotheses.
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