<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  <a href="margrel1.html#V2" target="_self">boolean</a>  <a href="hidden.html#M1">set</a> ;<br/>



<b>thus </b><a NAME="E1:39"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="margrel1.html#K10" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8" target="_self">TRUE</a>  implies ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8" target="_self">TRUE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8" target="_self">TRUE</a>  ) )
 <b>by </b><i><a class="ref" href="margrel1.html#D17" target="_self">Def17</a></i>;<br/>

<b>thus </b><a NAME="E2:39"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8" target="_self">TRUE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8" target="_self">TRUE</a>  implies <font color="Maroon">c<sub>1</sub></font> <a href="margrel1.html#K10" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8" target="_self">TRUE</a>  )
 <b>by </b><i><a class="ref" href="margrel1.html#D17" target="_self">Def17</a></i>;<br/>

<b>thus </b><a NAME="E3:39"/>
(  not <font color="Maroon">c<sub>1</sub></font> <a href="margrel1.html#K10" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7" target="_self">FALSE</a>  or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7" target="_self">FALSE</a>  or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7" target="_self">FALSE</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:39_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="margrel1.html#K10" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7" target="_self">FALSE</a> 
 ;<br/>

<a NAME="E2:39_1"/><b>then </b>
(  not <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8" target="_self">TRUE</a>  or  not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8" target="_self">TRUE</a>  )
 
<b>by </b><i><a class="ref" href="margrel1.html#D17" target="_self">Def17</a></i>;<br/>
<b>hence </b><a NAME="E3:39_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7" target="_self">FALSE</a>  or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7" target="_self">FALSE</a>  )
 <b>by </b><i><a class="ref" href="margrel1.html#T39" target="_self">Th39</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E4:39"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7" target="_self">FALSE</a>  or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7" target="_self">FALSE</a>  )
 ;<br/>

<b>hence </b><a NAME="E5:39"/>
<font color="Maroon">c<sub>1</sub></font> <a href="margrel1.html#K10" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7" target="_self">FALSE</a> 
 <b>by </b><i><a class="ref" href="margrel1.html#D17" target="_self">Def17</a></i>;<br/>


</div>
