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<b>let </b><font color="Maroon">x</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="unialg_1.html#V1">homogeneous</a> <a href="unialg_1.html#V2">quasi_total</a> <a href="partfun1.html#NM1">PartFunc</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="finseq_2.html#K3">*</a> ,<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span>, <font color="Maroon">y</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="unialg_1.html#V1">homogeneous</a> <a href="unialg_1.html#V2">quasi_total</a> <a href="partfun1.html#NM1">PartFunc</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="finseq_2.html#K3">*</a> ,<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:3_1_2"/><i><font color="Green">E75</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">f1</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>and </b><br/><a NAME="E2:3_1_2"/><i><font color="Green">E76</font></i>: 
for <font color="Olive">h</font> being   <a href="finseq_1.html#M2">FinSequence</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span>  st <font color="Olive">h</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">x</font> holds <br/><font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Olive">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K1" target="_self">pr1</a> <font color="Olive">h</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K2" target="_self">pr2</a> <font color="Olive">h</font></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E3:3_1_2"/><i><font color="Green">E77</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K3">arity</a> <font color="Maroon">f1</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>and </b><br/><a NAME="E4:3_1_2"/><i><font color="Green">E78</font></i>: 
for <font color="Olive">h</font> being   <a href="finseq_1.html#M2">FinSequence</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span>  st <font color="Olive">h</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">y</font> holds <br/><font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <font color="Olive">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K1" target="_self">pr1</a> <font color="Olive">h</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K2" target="_self">pr2</a> <font color="Olive">h</font></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="finseq_2.html#M2">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="finseq_2.html#K3">*</a> ;<br/><b>reconsider </b><font color="Maroon">c'</font> = <font color="Maroon">c</font> as    <a href="finseq_1.html#M2">FinSequence</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span> ;<br/><b>assume </b><a NAME="E2:3_1_2_1"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">x</font>
 ;<br/><a NAME="E3:3_1_2_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c'</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K1" target="_self">pr1</a> <font color="Maroon">c'</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K2" target="_self">pr2</a> <font color="Maroon">c'</font></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c'</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K1" target="_self">pr1</a> <font color="Maroon">c'</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><a href="pralg_1.html#K2" target="_self">pr2</a> <font color="Maroon">c'</font></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i>, , , </i>;<br/><b>hence </b><a NAME="E4:3_1_2_1"/>
<font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:3_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, , <a class="ref" href="partfun1.html#T34">PARTFUN1:34</a></i>;<br/>


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