theorem :: BOOLE'53:

: theorem :: BOOLE'45: : xboole1.miz : theorem :: BOOLE'44: 目次

theorem :: BOOLE'53:

theorem :: BOOLE'53:
  (X /\ Y) \/ (X /\ Z) c= Y \/ Z
proof
  now let x;
    assume x in (X /\ Y) \/ (X /\ Z);
    then x in (X /\ Y) or x in (X /\ Z) by XBOOLE_0:def 2;
    then (x in X & x in Y) or (x in X & x in Z) by XBOOLE_0:def 3;
    hence x in Y \/ Z by XBOOLE_0:def 2;
  end;
  hence thesis by TARSKI:def 3;
end;

　これは以下の通りです。

$\begin{displaymath} (X \cap Y) \cup (X \cap Z) \subseteq Y \cup Z \end{displaymath}$

証明　

$\begin{eqnarray*}　　&&xを任意にとり, x \in (X \cap Y) \cup (X \cap Z)を仮定�... ...:def 3から\\ &&(X \cap Y) \cup (X \cap Z) \subseteq Y \cup Z \end{eqnarray*}$

証明終了

Yasunari SHIDAMA