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<b>let </b><font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="funct_3.html#K12" title="FUNCT_3:func.12">delta</a> <font color="Maroon" title="c1">X</font></span>)</span> or  not <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="funct_3.html#K12" title="FUNCT_3:func.12">delta</a> <font color="Maroon" title="c1">X</font></span>)</span> or  not <span class="p1">(<span class="default"><a href="funct_3.html#K12" title="FUNCT_3:func.12">delta</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="funct_3.html#K12" title="FUNCT_3:func.12">delta</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x2</font> or <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font> )</span><br/>

<b>set </b><font color="Maroon" title="c4">f</font> =  <a href="funct_3.html#K12" title="FUNCT_3:func.12">delta</a> <font color="Maroon" title="c1">X</font>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:5_1_1"/><i><font color="Green" title="E5">A1</font></i>: 
<font color="Maroon" title="c2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="funct_3.html#K12" title="FUNCT_3:func.12">delta</a> <font color="Maroon" title="c1">X</font></span>)</span>
 <b>and </b><br/><a NAME="E2:5_1_1"/><i><font color="Green" title="E6">A2</font></i>: 
<font color="Maroon" title="c3">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="funct_3.html#K12" title="FUNCT_3:func.12">delta</a> <font color="Maroon" title="c1">X</font></span>)</span>
 <b>and </b><br/><a NAME="E3:5_1_1"/><i><font color="Green" title="E7">A3</font></i>: 
<span class="p1">(<span class="default"><a href="funct_3.html#K12" title="FUNCT_3:func.12">delta</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="funct_3.html#K12" title="FUNCT_3:func.12">delta</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font></span><br/>

<a NAME="E4:5_1_1"/><i><font color="Green" title="E8">A4</font></i>: 
<span class="p1">(<span class="default"><a href="funct_3.html#K12" title="FUNCT_3:func.12">delta</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c2">x1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 
<b>by </b><i><a class="txt" href="#E1:5_1_1"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="funct_3.html#D7" title="FUNCT_3:def.7">FUNCT_3:def 7</a></i>;<br/>
<a NAME="E5:5_1_1"/>
<span class="p1">(<span class="default"><a href="funct_3.html#K12" title="FUNCT_3:func.12">delta</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c3">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 
<b>by </b><i><a class="txt" href="#E2:5_1_1"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="funct_3.html#D7" title="FUNCT_3:def.7">FUNCT_3:def 7</a></i>;<br/>
<b>hence </b><a NAME="E6:5_1_1"/>
<font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font>
 <b>by </b><i><a class="txt" href="#E3:5_1_1"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="#E4:5_1_1"><i><font color="Green" title="E8">A4</font></i></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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