Exercise logic.propositional.consequence

Description
Prove that formula is a logical consequence of a set of formulas

Derivation

((p /\ q) || (~p /\ ~q)) /\ p => q

⇒ logic.propositional.oroverand, initial=TList [TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar "p",TVar "q"],TCon logic1.and [TCon logic1.not [TVar "p"],TCon logic1.not [TVar "q"]]],TVar "p"]]

((p /\ q) || ~p) /\ ((p /\ q) || ~q) /\ p => q

⇒ logic.propositional.oroverand

(p || ~p) /\ (q || ~p) /\ ((p /\ q) || ~q) /\ p => q

⇒ logic.propositional.complor

T /\ (q || ~p) /\ ((p /\ q) || ~q) /\ p => q

⇒ logic.propositional.oroverand

T /\ (q || ~p) /\ (p || ~q) /\ (q || ~q) /\ p => q

⇒ logic.propositional.complor

T /\ (q || ~p) /\ (p || ~q) /\ T /\ p => q

⇒ logic.propositional.truezeroand

(q || ~p) /\ (p || ~q) /\ T /\ p => q

⇒ logic.propositional.truezeroand

(q || ~p) /\ (p || ~q) /\ p => q

⇒ logic.propositional.absorpand

(q || ~p) /\ p => q

⇒ fakeabsorption

q /\ p => q

⇒ conj-elim

q => q