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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  <a href="margrel1.html#V2">boolean</a>  <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><a NAME="E1:23"/><i><font color="Green">E4</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>2</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="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 ;<br/>

<div><i><font color="Green">E5</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:23_1"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 ;<br/><i><font color="Green">E7</font></i>: <font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>2</sub></font> = 
<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>

<br/>.= 
<a href="margrel1.html#K7">FALSE</a>  <a href="binarith.html#K1">'or'</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="binari_5.html#E1:23_1"><i><font color="Green">E6</font></i></a>, <a class="ref" href="margrel1.html#T41">MARGREL1:41</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="binarith.html#T7">BINARITH:7</a></i>
;<br/><font color="Maroon">c<sub>2</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>3</sub></font> = 
<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="binarith.html#K1">'or'</a> <font color="Maroon">c<sub>3</sub></font>

<br/>.= 
<a href="margrel1.html#K7">FALSE</a>  <a href="binarith.html#K1">'or'</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="binari_5.html#E1:23"><i><font color="Green">E4</font></i></a>, <a class="txt" href="binari_5.html#E2:23_1"><i><font color="Green">E7</font></i></a>, <a class="ref" href="margrel1.html#T41">MARGREL1:41</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="binarith.html#T7">BINARITH:7</a></i>
;<br/><a NAME="E4:23_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <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> <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i><a class="txt" href="binari_5.html#E1:23"><i><font color="Green">E4</font></i></a></i>;<br/><b>hence </b><a NAME="E5:23_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>3</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>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:23_2"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="margrel1.html#K8">TRUE</a> 
 ;<br/><font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>3</sub></font> = 
<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>3</sub></font>

<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <a href="margrel1.html#K7">FALSE</a> </span>)</span> <a href="binarith.html#K1">'or'</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="binari_5.html#E1:23_2"><i><font color="Green">E6</font></i></a>, <a class="ref" href="margrel1.html#T39">MARGREL1:39</a></i>
<br/>.= 
<a href="margrel1.html#K8">TRUE</a>  <a href="binarith.html#K1">'or'</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="margrel1.html#T41">MARGREL1:41</a></i>
;<br/><b>hence </b><a NAME="E3:23_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>3</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="E4:23"/>
<font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i><a class="txt" href="binari_5.html#E2:23"><i><font color="Green">E5</font></i></a></i>;<br/>


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