# Justify each step in the proof sequence

$[A \rightarrow ( B \lor C) ] \land B' \land C' \rightarrow A'$

I know how to read the proof sequence, but I don't know what it means to "justify" each step? Does this mean to just state what each step is doing?

1.) $A \rightarrow (B \lor C)$

2.) $B'$

3.) $C'$

4.) $B' \land C'$

5.) $(B \lor C)'$

6.) $A'$

Not looking for answers, but any guidance is appreciated.

Normally by justify it means that at each step of the way you would put a short reason of why you made that move.

So for an example :

1) $a(b+c)$

2) $ab+ac$ (Distributive property)

Just something like that.

It means to produce an "annotated" proof, with indication of the rules of inference used in each step, like the following for, e.g. :

$[(A→B)∧A] → (B∨C)$

1) $(A→B)∧A$ --- assumption

2) $(A→B)$ --- from 1 ) by $\land$-elimination

3) $A$ --- from 1 ) by $\land$-elimination

4) $B$ --- from 3) and 2) by $\rightarrow$-elimination [i.e. modus ponens]

5) $(B∨C)$ --- from 4) by $\lor$-introduction

6) $[(A→B)∧A] \rightarrow (B∨C)$ --- from 1) and 5) by $\rightarrow$-introduction [i.e. Deduction Theorem].