If you are a coauthor you can get started by adding some content to it. Click the Insert or Insert Figure button below or drag and drop an image onto this text.

Lemma 4.3
and Theorem 4.5 provide a method to construct a proof for a given tautology in
terms of the axioms of AXSP3B, as we show next with an example.

this is for holding javascript data

this is a placeholder for an editor

this is for holding javascript data

this is a placeholder for an editor

Example.
The formula $ p \vee (\neg (p \wedge
\neg p)) $ is a tautology as shown by its true table. The formula is a
disjunction, we put $ \eta = (\neg (p \wedge \neg p) $ . We prove that this
formula is a Theorem by using Lemma 4.3.

this is for holding javascript data

this is a placeholder for an editor

Let $ \nu $
be a Valuation such that $ \nu (p)=0 $ , then $ \nu (\eta )=2 $. According to
case 2 (e) of Lemma 4.3 $ \neg (p \wedge p) \vdash \neg (p \wedge p) $ and $ \neg (p \wedge p)
\vdash \neg (\neg \eta \wedge \neg \eta
)$

this is for holding javascript data

this is a placeholder for an editor

According
to axiom PB10 $ \neg (\neg \eta \wedge \neg \eta )) \wedge \neg (p \wedge p)
\rightarrow \neg (\neg (\eta \vee p) \wedge \neg (\eta \vee p)) $. According to
axiom PB1