Axiomatic Semantics and Postconditions I'll preface this by saying that this IS a homework question.

However, when asked about how to solve it in class, (I believe) my professor was unable to complete it.

The question is: 


  Compute the weakest precondition for each of the following 
  assignment statements and postconditions:
  $$a = a + 2b - 1\ \{a &gt; 1\}$$ (where a > 1 is the postcondition)


His answer was: "$a &gt; 2 - 2b$."
Is this correct? It seems that he broke the rules of equivalents, by using the ">" as "="

I believe the answer is:
$$\{a&gt;1\;\wedge\; b&lt;\tfrac12\}\quad\text{or}\quad \{a &gt; 0\;\wedge\;2b-1 +a &gt;1\},$$ 
    where the "$\wedge$" symbol means "and"

We're using Concepts of Programming Languages, by Sebesta, 10th Edition, so any references from that material would be excellent :)

Thanks!
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.