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<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font>, <font color="Maroon" title="c3">X'</font>, <font color="Maroon" title="c4">Y'</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c5">f</font>, <font color="Maroon" title="c6">g</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>











<b>assume </b><a NAME="E1:62"/><i><font color="Green" title="E38">A1</font></i>: 
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c6">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">X'</font>,<font color="Maroon" title="c4">Y'</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 ;<br/>

<b>hence </b><a NAME="E2:62"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1"><a href="funct_4.html#K3" title="FUNCT_4:func.3">|:</a><span class="default"><font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font></span><a href="funct_4.html#K3" title="FUNCT_4:func.3">:|</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">X'</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">Y</font>,<font color="Maroon" title="c4">Y'</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="ref" href="funct_4.html#T60" target="_self" title="FUNCT_4:th.60">Th60</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><br/>

<b>let </b><font color="Maroon" title="c7">z</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="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E3:62"/>
<font color="Maroon" title="c7">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">X'</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">Y</font>,<font color="Maroon" title="c4">Y'</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c8">xx</font>, <font color="Maroon" title="c9">yy</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:62"/><i><font color="Green" title="E39">A2</font></i>: 
<font color="Maroon" title="c8">xx</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">X'</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>and </b><br/><a NAME="E6:62"/><i><font color="Green" title="E40">A3</font></i>: 
<font color="Maroon" title="c9">yy</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">Y</font>,<font color="Maroon" title="c4">Y'</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>and </b><br/><a NAME="E7:62"/><i><font color="Green" title="E41">A4</font></i>: 
<font color="Maroon" title="c7">z</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="c8">xx</font>,<font color="Maroon" title="c9">yy</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">x</font>, <font color="Maroon" title="c11">x'</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E9:62"/><i><font color="Green" title="E42">A5</font></i>: 
( <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c11">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X'</font> )
 <b>and </b><br/><a NAME="E10:62"/><i><font color="Green" title="E43">A6</font></i>: 
<font color="Maroon" title="c8">xx</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="c10">x</font>,<font color="Maroon" title="c11">x'</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="txt" href="funct_4.html#E5:62"><i><font color="Green" title="E39">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c12">y</font>, <font color="Maroon" title="c13">y'</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E12:62"/><i><font color="Green" title="E44">A7</font></i>: 
( <font color="Maroon" title="c12">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c13">y'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y'</font> )
 <b>and </b><br/><a NAME="E13:62"/><i><font color="Green" title="E45">A8</font></i>: 
<font color="Maroon" title="c9">yy</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="c12">y</font>,<font color="Maroon" title="c13">y'</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="txt" href="funct_4.html#E6:62"><i><font color="Green" title="E40">A3</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<a NAME="E14:62"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c12">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">f</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">x'</font>,<font color="Maroon" title="c13">y'</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c6">g</font> )
 
<b>by </b><i><a class="txt" href="funct_4.html#E1:62"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="funct_4.html#E9:62"><i><font color="Green" title="E42">A5</font></i></a>, <a class="txt" href="funct_4.html#E12:62"><i><font color="Green" title="E44">A7</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>hence </b><a NAME="E15:62"/>
<font color="Maroon" title="c7">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1"><a href="funct_4.html#K3" title="FUNCT_4:func.3">|:</a><span class="default"><font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font></span><a href="funct_4.html#K3" title="FUNCT_4:func.3">:|</a></span>
 <b>by </b><i><a class="txt" href="funct_4.html#E7:62"><i><font color="Green" title="E41">A4</font></i></a>, <a class="txt" href="funct_4.html#E10:62"><i><font color="Green" title="E43">A6</font></i></a>, <a class="txt" href="funct_4.html#E13:62"><i><font color="Green" title="E45">A8</font></i></a>, <a class="ref" href="funct_4.html#D3" target="_self" title="FUNCT_4:def.3">Def3</a></i>;<br/>


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