theorem :: BOOLE'68:

: theorem BOOLE'69: :: BOOLE'69: : xboole1.miz : theorem :: BOOLE'57: 目次

theorem :: BOOLE'68:

theorem :: BOOLE'68:
  X /\ (X \/ Y) = X
proof
  thus X /\ (X \/ Y) c= X
  proof let x;
    thus thesis by XBOOLE_0:def 3;
  end;
  let x;
  assume x in X;
  then x in X & x in X \/ Y by XBOOLE_0:def 2;
  hence thesis by XBOOLE_0:def 3;
end;

　これは以下の通りです。

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

証明　

$\begin{eqnarray*}　 &&先ず,(1)~~X \cap (X \cup Y) \subseteq X \\ &&~~(1)の�... ...&&故にXBOOLE\_0:def 3から\\ &&X \subseteq X \cap (X \cup Y) \end{eqnarray*}$

証明終了

Yasunari SHIDAMA