这是一份oxford牛津大学作业代写的成功案例
Here $\alpha \vee \beta$ depends on the same assumptions on which $\alpha$, or $\beta$, depends. So IV is used as follows:
$x \quad(n) \quad \alpha$
$x \quad(m) \quad \alpha \vee \beta \quad \operatorname{I\vee n}$
Or alternatively:
$x \quad(n) \quad \beta$
$x \quad(m) \quad \alpha \vee \beta \quad \operatorname{IV} n$
The right number $n$ indicates the line of $\alpha$, or $\beta$. The left numbers, instead, are the same as those of $\alpha$, or $\beta$. For example, IV is used in the following derivation of $\sim p \vee q$ from $p \supset q$ :
1 (1) $p \supset q \quad \mathrm{~A}$
$2 \quad$ (2) $\sim(\sim p \vee q) \quad \mathrm{A}$
$3 \quad$ (3) $p$ A
Oxford COURSE NOTES ：
you may start as follows:
1 (1) $p \wedge q \quad \mathrm{~A}$
2 (2) q $r \mathrm{~A}$
The second step is to write $\alpha$ at the end of the derivation, for $\alpha$ must occur as the last formula. Thus, in our example you may write $p \wedge r$ at the end of the sequence:
$1 \quad$ (1) $p \wedge q \quad \mathrm{~A}$
2 (2) $q \supset r \quad \mathrm{~A}$
() $p \wedge r$