I'm trying to write a question about natural dedcution, but I'm not sure what the best/easiest way is to write something similar to this at MSE:
In this post, I tried this:
- $\lnot (p \lor \lnot p) \quad \quad \quad (H)$
- $p \quad \quad \quad \quad \quad (H)$
- $p \lor \lnot p \quad \quad \; \;(\lor \text{I} 2)$
- $ \bot \quad \quad \quad \quad \;\;(\lnot \text{E}1,3)$
- $\lnot p \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \; (\lnot \text{I}2 - 4)$
- $p \lor \lnot p \;\;\;\;\;\;\;\;\; \;\;\;\;\;\,(\lor \text{I}5)$
- $\bot \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\,(\lnot \text{E}1,6)$
- $p \lor \lnot p \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\,\;\;\;(\bot \text{E}1-7)$
I think that this solution is not that bad, but using all those \;
to align thinks is a little tedious. Does somebody has another/better solution to write natural deduction proofs at MSE ?