Exercise logic.propositional.consequence
Description
Prove that formula is a logical consequence of a set of formulas
Derivation
![](http://ideas.cs.uu.nl/images/external.png)
~q => (p || (~(p || q) /\ ~p)) /\ (p || q || (~(p || q) /\ ~p))
⇒ logic.propositional.demorganor, initial=TList [TCon logic1.not [TVar "q"]]~q => (p || (~(p || q) /\ ~p)) /\ (p || q || (~p /\ ~q /\ ~p))
⇒ logic.propositional.genoroverand~q => (p || (~(p || q) /\ ~p)) /\ (p || ((q || ~p) /\ (q || ~q) /\ (q || ~p)))
⇒ logic.propositional.complor~q => (p || (~(p || q) /\ ~p)) /\ (p || ((q || ~p) /\ T /\ (q || ~p)))
⇒ logic.propositional.truezeroand~q => (p || (~(p || q) /\ ~p)) /\ (p || ((q || ~p) /\ (q || ~p)))
⇒ logic.propositional.idempand~q => (p || (~(p || q) /\ ~p)) /\ (p || q || ~p)