Axiomatic Semantics and Postconditions
A condition $P$ is weaker than $Q$ if $Q\Rightarrow P$; that is, whenever $Q$ holds, $P$ also holds or, if you prefer, $Q$ guarantees that $P$ holds. $P$ is strictly weaker than $Q$ if $Q\Rightarrow P$ but $P\not\Rightarrow Q$.  Let's look at the three conditions included in the question:


$a&gt;2-2b$
$a&gt;1 \;\wedge\;b&gt;\tfrac12$
$a&gt;0 \;\wedge\; a&gt;2-2b$


(2)&nbsp;$\Rightarrow$&nbsp;(3) since, if $a&gt;1$ then certianly $a&gt;0$ and, if $b&gt;\tfrac12$, then $2-2b&lt;1&lt;a$. (3)&nbsp;$\Rightarrow$&nbsp;(1) since if $X$ and something else are both true, then certainly $X$&nbsp;is true. None of the reverse implications holds: (1)&nbsp;is satisfied by $a=-1$, $b=2$ but (3)&nbsp;is not; (3)&nbsp;is satisfied by $a=\tfrac12$, $b=1$ but (2)&nbsp;is not. Therefore, (1) is strictly weaker than (3) which, in turn, is strictly weaker than&nbsp;(2).

So $a&gt;2-2b$ is the weakest of the preconditions on the table. But is it the weakest possible? Suppose $P$&nbsp;is any precondition that implies that $a+2b-1&gt;1$.  Rearranging, we see that $P\Rightarrow a&gt;2-2b$, i.e., $P\Rightarrow$&nbsp;(1). This tells us that no other precondition can be strictly weaker than&nbsp;(1). Therefore, (1)&nbsp;is the weakest precondition.

I don't understand what you mean by `It seems that he broke the rules of equivalents, by using the ">" as "="' since, surely, if (1) breaks that rule, (3) does too? I don't know that rule so maybe somebody else can address that part of the question.