Say we have a (positively) real valued logic, i.e. formulas evaluate to the extended interval $[0,\, \infty]$. Furthermore, we have a Gödel implication $a \rightarrow b$ that evaluates to $\infty$ wherever $a$ evaluates to something less-than or equal $b$, and to $b$ otherwise, i.e. the semantics $[[a \rightarrow b]]$ of the Gödel implication under a model $m$ is given by
$$[[ a \rightarrow b]](m) ~{}={}~ \begin{cases}\infty~, & \text{if } [[ a ]](m) \leq [[b]](m)\\ [[b]](m)~, & \text{otherwise.}\end{cases}$$

In classical logic, we can think of $a \rightarrow \:{\cdot}\:$ as a kind of "assume $a$" operation. How can we think of $5 \rightarrow x^2$ as a kind of "assume 5"? How is $5 \rightarrow x^2$ an assumption of $5$ on $x^2$?