Exercise logic.propositional.dnf

Description
Proposition to DNF

Derivation

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

⇒ logic.propositional.idempand

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

⇒ logic.propositional.falsezeroand

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

⇒ logic.propositional.idempand

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

⇒ logic.propositional.notfalse

(T -> (~~(F /\ r) || q)) || ~~p

⇒ logic.propositional.notnot

(T -> ((F /\ r) || q)) || ~~p

⇒ logic.propositional.falsezeroand

(T -> (F || q)) || ~~p

⇒ logic.propositional.falsezeroor

(T -> q) || ~~p

⇒ logic.propositional.defimpl

~T || q || ~~p

⇒ logic.propositional.notnot

~T || q || p

⇒ logic.propositional.nottrue

F || q || p

⇒ logic.propositional.falsezeroor

q || p