How to prove $c = a + b$ using Program Verification Techniques
We can prove the Hoare triple

\begin{align}
  \{{\sf true}\}\\
  c = a + b\\
  \{c = a + b\}
\end{align}

using the assignment rule. We take the postcondition $c = a + b$ and we substitute backwards $\{(a+b)/c\}$, so we get $(c = a + b)\{(a+b)/c\} = (a+b=a+b)$. That's the weakest precondition. Hence, we proved

\begin{align}
  \{a+b = a+b\}\\
  c = a + b\\
  \{c = a + b\}
\end{align}

We can then use the weakening/strengthening/pre-post rule to rewrite $a+b=a+b$ as $\sf true$, since they are equivalent logical formulae.