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

<a NAME="E1:5_1_1"/><i><font color="Green">E1</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1 )
 
<b>by </b><i><a class="ref" href="margrel1.html#T39">MARGREL1:39</a></i>;<br/>
<a NAME="E2:5_1_1"/><i><font color="Green">E2</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1 )
 
<b>by </b><i><a class="ref" href="margrel1.html#T39">MARGREL1:39</a></i>;<br/>
<a NAME="E3:5_1_1"/>
( <span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K1">'or'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  iff ( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  ) ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:5_1_1_1"/><i><font color="Green">E3</font></i>: 
( ( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  ) ) implies <span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K1">'or'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:5_1_1_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  implies <span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K1">'or'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:5_1_1_1_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  )
 ;<br/>

<a NAME="E2:5_1_1_1_1_1"/><b>then </b>
 <a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 
<b>by </b><i><a class="ref" href="margrel1.html#D16">MARGREL1:def 16</a></i>;<br/>
<b>hence </b><a NAME="E3:5_1_1_1_1_1"/>
<span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K1">'or'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i><a class="ref" href="binarith.html#T19">BINARITH:19</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:5_1_1_1_1"/>
( ( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  ) ) implies <span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K1">'or'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 <b>by </b><i><a class="ref" href="binarith.html#T19">BINARITH:19</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:5_1_1_1"/><i><font color="Green">E4</font></i>: 
(  not <span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K1">'or'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  or  <a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:5_1_1_1_2"/><i><font color="Green">E5</font></i>: 
<span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K1">'or'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 ;<br/>

<a NAME="E2:5_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K1">'or'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9">'not'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="binarith.html#D1">BINARITH:def 1</a></i>;<br/>
<a NAME="E3:5_1_1_1_2"/><b>then </b>
 <a href="margrel1.html#K9">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 
<b>by </b><i><a class="txt" href="bvfunc_1.html#E1:5_1_1_1_2"><i><font color="Green">E5</font></i></a></i>;<br/>
<a NAME="E4:5_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="margrel1.html#K10">'&amp;'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 
<b>by </b><i><a class="ref" href="margrel1.html#T41">MARGREL1:41</a></i>;<br/>
<a NAME="E5:5_1_1_1_2"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  or  <a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  )
 
<b>by </b><i><a class="ref" href="margrel1.html#T45">MARGREL1:45</a></i>;<br/>
<b>hence </b><a NAME="E6:5_1_1_1_2"/>
(  <a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 <b>by </b><i><a class="ref" href="margrel1.html#T41">MARGREL1:41</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:5_1_1_1"/>
( <!--HUMANRECFAILED-->( ( not  <a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  &amp; not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  ) ) &amp; ( ( not <!--HUMANRECFAILED-->( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  ) ) or  <a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) )
 
<b>by </b><i><a class="ref" href="margrel1.html#T39">MARGREL1:39</a>, <a class="ref" href="margrel1.html#T41">MARGREL1:41</a></i>;<br/>
<b>hence </b><a NAME="E4:5_1_1_1"/>
( <span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K1">'or'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  iff ( ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  ) ) )
 <b>by </b><i><a class="txt" href="bvfunc_1.html#E1:5_1_1_1"><i><font color="Green">E3</font></i></a>, <a class="txt" href="bvfunc_1.html#E2:5_1_1_1"><i><font color="Green">E4</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:5_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#NR1" target="_self">'&lt;'</a> <font color="Maroon">c<sub>2</sub></font> iff <font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K1" target="_self">'imp'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 <b>by </b><i><a class="txt" href="bvfunc_1.html#E1:5_1_1"><i><font color="Green">E1</font></i></a>, <a class="txt" href="bvfunc_1.html#E2:5_1_1"><i><font color="Green">E2</font></i></a></i>;<br/>


</div>
