Often times in mathematics writing, authors prove the two sides of the implication by showing a proof of necessity and a proof of sufficiency, and the proof takes the following template:
Proposition: $A$ if and only if $B$
Proof.
(Necessity) [... proof of $A \implies B$ here ...](Sufficiency) [... proof of $B \implies A$ here ...]
My question is: on what basis does the writer use (Sufficiency) used to mean $B \implies A$ and (Necessity) to mean $A \implies B$? The choice seems rather arbitrary, as one can write the implication $A \implies B$ as either "$A$ is sufficient for $B$" or as "$B$ is necessary for $A$".
Is there a consistent pattern where writers typically choose "sufficient" and "necessary" both in reference to $A$ because $A$ appeared first in the statement of the Proposition?