Section club.
Variable Scottish RedSocks WearKilt Married GoOutSunday : Prop.
Hypothesis rule1 : ~ Scottish -> RedSocks.
Hypothesis rule2 : WearKilt \/ ~ RedSocks.
Hypothesis rule3 : Married -> ~ GoOutSunday.
Hypothesis rule4 : GoOutSunday <-> Scottish.
Hypothesis rule5 : WearKilt -> Scottish /\ Married.
Hypothesis rule6 : Scottish -> WearKilt.
tauto.
Qed.
End club.
tauto.
Qed.
tauto.
Qed.
tauto.
Qed.
tauto.
Qed.
tauto.
Qed.
tauto.
Qed.
tauto.
Qed.
tauto.
Qed.
tauto.
Qed.
tauto.
Qed.
tauto.
Qed.

Theorem y3 : forall x0 : A /\ B, B /\ A.