I am tryingto teach myself formal proofs in the system F. I have been using the text Language Proof and Logic in my attempts at learning predicate logic and the fundamentals of logic in general.
I’ve been working steadily through this material, however, I am struggling with formal proof of the distrubution rule, withut the aid of tautological consequence.
I’m not sure if this question is against the rules, but I will ask anyway. May this post be deleted if it is against the rules.
I am having trouble proving A v (B&C) from the premises AvB and AvC
I have attempted to complete this prood using a proof by contradiction, however, in every iteration I attempt, I arrive at the need for the use of tautological consequence as the justification for some step in my proof.
How can I circumvent an appeal to tautological consequence? Since, afterall, Av(B&C) is a tautological consequence of AvC and AvB in its own right.