It's homework, so I won't give the example, but when is it legal for me to discharge an assumption? Basically, I'm introducing a conditional to prove a theorem that does not rest on any assumptions, and I want to make sure the consequent follows from the antecedent. But, I had to use two reductio ad absurdum arguments to get there, and I feel like I'm stuck with an assumption that was necessary to set up the contradiction. Any advice, or should I just keep at it? Is it legal to include the main assumption in the line that has the contradiction in an reductio ad absurdum argument???
My Professor answered the question about whether lines 1-4 were legal, but he did not get back to me regarding how legal lines (11) and (12) were (90 students worth of homework to grade probably).
Any guidance on how to discharge all my premises or any rules to look at in the Fitch style with the limitations my professor gave us??
Also, I'm not allowed to sequent introduction or use theorem introduction.
I'm having trouble making sure not only that the consequents of every conditional I introduce is generated by the antecedent + making sure that line (1) plays a role in generating line (11) while discharging all my assumptions.
Ultimately, line 12 not resting on any assumptions seems wrong by the way I did it. Please help.
That's basically my problem.
Thanks LemonTree!! I was able to make a formal proof for it.[
Also, Lemontree, I added line I was missing, and I fixed the furthermost right column. Thanks!