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<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="valuat_1.html#V1">boolean-valued</a> <a href="funct_1.html#NM1">Function</a>;<br/>

<a NAME="E1:21"/><i><font color="Green">E12</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K3">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="valuat_1.html#D3">VALUAT_1:def 3</a></i>;<br/>
<a NAME="E2:21"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K3">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds <br/><font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</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="valuat_1.html#K3">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:21_1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K3">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/>

<b>thus </b><font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> = 
 <a href="margrel1.html#K9">'not'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>

<br/>.= 
 <a href="margrel1.html#K9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K3">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="bvfunc_1.html#E1:21"><i><font color="Green">E12</font></i></a>, <a class="txt" href="bvfunc_1.html#E1:21_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="valuat_1.html#D3">VALUAT_1:def 3</a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:21"/>
 <a href="valuat_1.html#K3">'not'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K3">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc_1.html#E1:21"><i><font color="Green">E12</font></i></a>, <a class="ref" href="valuat_1.html#D3">VALUAT_1:def 3</a></i>;<br/>


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