Exercise logic.propositional.consequence

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

Derivation

p -> (p -> q), p => q

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

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

⇒ logic.propositional.defimpl

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

⇒ logic.propositional.defimpl

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

⇒ logic.propositional.idempor

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

⇒ fakeabsorption

q /\ p => q

⇒ conj-elim

q => q