Exercise logic.propositional.consequence

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

Derivation

p -> q, p -> r => p -> (q /\ r)

⇒ conj-intro, initial=TList [TCon logic1.implies [TVar "p",TVar "q"],TCon logic1.implies [TVar "p",TVar "r"]]

(p -> q) /\ (p -> r) => p -> (q /\ r)

⇒ logic.propositional.defimpl

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

⇒ logic.propositional.defimpl

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

⇒ logic.propositional.defimpl

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

⇒ logic.propositional.oroverand

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