Also, If I am working on a demonstration and the conclusion is an 'or statement' such as: ~p OR q
and I have proven that ~p, then does that means that I have completed my proof...? How would I write that as a step in the demonstration? b/c I am not suppose to use the conclusion as part of my proof. So once I reach the part of the proof where ~p, that is part of my conclusion, since (conclusion: ~p OR q). So am I done once I reach either ~p or q?
For example (conclusion: ~p OR t):
p OR q
(would I add a separate step for the conclusion, or add another line here and write therefore AGAIN and then write ~p or t, since the conclusion is reached...??)