Why is an assumption not discharged for the first implication introduction in natural deduction?

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Why is it that an assumption need not be discharged for the first implication introduction in natural deduction?

For example,

$$\dfrac{\dfrac{[p]^1}{q\to p}{{\to}\mathrm I}}{p\to(q\to p)}{{\to}\mathrm I^1}$$

Why is it q need not be discharged like p?

Example 1

Example 2