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 /\ q /\ p) || (~(p /\ q) /\ ~p)
⇒ logic.propositional.demorganandq => (p /\ q /\ p) || ((~p || ~q) /\ ~p)
⇒ logic.propositional.absorpandq => (p /\ q /\ p) || ~p
⇒ logic.propositional.genoroverandq => (p || ~p) /\ (q || ~p) /\ (p || ~p)
⇒ logic.propositional.complorq => T /\ (q || ~p) /\ (p || ~p)
⇒ logic.propositional.complorq => T /\ (q || ~p) /\ T
⇒ logic.propositional.truezeroandq => (q || ~p) /\ T
⇒ logic.propositional.truezeroandq => q || ~p
⇒ commor.sortq => ~p || q
⇒ introfalseleftF || q => ~p || q
⇒ introcompl(p /\ ~p) || q => ~p || q
⇒ logic.propositional.oroverand(p || q) /\ (~p || q) => ~p || q
⇒ conj-elim~p || q => ~p || q