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<b>let </b><font color="Maroon">f</font> be   <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">g</font> be   <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">h</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>

<div><i><font color="Green">E16</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:4_1_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_4.html#K2">~</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">h</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K15">:]</a></span></span>)</span>
 ;<br/><a NAME="E2:4_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">h</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K15">:]</a></span>
 <b>by </b><i><a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/><a NAME="E3:4_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">h</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="funct_3.html#D9">FUNCT_3:def 9</a></i>;<br/><b>then consider </b><font color="Maroon">y1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">z1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:4_1_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">y1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">h</font>
 <b>and </b><br/><a NAME="E6:4_1_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">z1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font>
 <b>and </b><br/><a NAME="E7:4_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y1</font>,<font color="Maroon">z1</font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T103">ZFMISC_1:103</a></i>;<br/><b>take </b><font color="Maroon">z1</font> = <font color="Maroon">z1</font>;<br/><b>take </b><font color="Maroon">y1</font> = <font color="Maroon">y1</font>;<br/><b>thus </b><a NAME="E8:4_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y1</font>,<font color="Maroon">z1</font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i/>;<br/><a NAME="E9:4_1_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">h</font></span><a href="funct_3.html#K15">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">h</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="funct_3.html#D9">FUNCT_3:def 9</a></i>;<br/><a NAME="E10:4_1_1"/><b>then </b><i><font color="Green">E29</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">z1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">h</font></span><a href="funct_3.html#K15">:]</a></span>
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><a NAME="E11:4_1_1"/><i><font color="Green">E30</font></i>: 
<span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">h</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K15">:]</a></span> <a href="binop_1.html#K1">.</a> <font color="Maroon">y1</font>,<font color="Maroon">z1</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">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z1</font></span>)</span></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i>, , <a class="ref" href="funct_3.html#D9">FUNCT_3:def 9</a></i>;<br/><a NAME="E12:4_1_1"/><i><font color="Green">E31</font></i>: 
<span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">h</font></span><a href="funct_3.html#K15">:]</a></span> <a href="binop_1.html#K1">.</a> <font color="Maroon">z1</font>,<font color="Maroon">y1</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">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y1</font></span>)</span></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i>, , <a class="ref" href="funct_3.html#D9">FUNCT_3:def 9</a></i>;<br/><a NAME="E13:4_1_1"/>
<span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">h</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K15">:]</a></span> <a href="binop_1.html#K1">.</a> <font color="Maroon">y1</font>,<font color="Maroon">z1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="funct_4.html#K2">~</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a>, </i>;<br/><a NAME="E14:4_1_1"/><b>then </b>
<span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">h</font></span><a href="funct_3.html#K15">:]</a></span> <a href="binop_1.html#K1">.</a> <font color="Maroon">z1</font>,<font color="Maroon">y1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 <b>by </b><i>, , <a class="ref" href="funct_4.html#T43">FUNCT_4:43</a></i>;<br/><b>hence </b><a NAME="E15:4_1_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">z1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">h</font></span><a href="funct_3.html#K15">:]</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/></div>
<b>end;</b></div><b>given </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">z</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><a NAME="E2:4_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">z</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E3:4_1"/><i><font color="Green">E33</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">h</font></span><a href="funct_3.html#K15">:]</a></span></span>)</span>
 ;<br/><a NAME="E4:4_1"/><i><font color="Green">E35</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">h</font></span><a href="funct_3.html#K15">:]</a></span>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/><a NAME="E5:4_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">h</font></span><a href="funct_3.html#K15">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">h</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="funct_3.html#D9">FUNCT_3:def 9</a></i>;<br/><a NAME="E6:4_1"/><b>then </b><i><font color="Green">E36</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">h</font> )
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><a NAME="E7:4_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">h</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K15">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">h</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="funct_3.html#D9">FUNCT_3:def 9</a></i>;<br/><a NAME="E8:4_1"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">h</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K15">:]</a></span>
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><a NAME="E9:4_1"/><i><font color="Green">E38</font></i>: 
<span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">h</font></span><a href="funct_3.html#K15">:]</a></span> <a href="binop_1.html#K1">.</a> <font color="Maroon">y</font>,<font color="Maroon">z</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">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i>, <a class="ref" href="funct_3.html#D9">FUNCT_3:def 9</a></i>;<br/><a NAME="E10:4_1"/><i><font color="Green">E39</font></i>: 
<span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">h</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K15">:]</a></span> <a href="binop_1.html#K1">.</a> <font color="Maroon">z</font>,<font color="Maroon">y</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">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font></span>)</span></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i>, <a class="ref" href="funct_3.html#D9">FUNCT_3:def 9</a></i>;<br/><a NAME="E11:4_1"/>
<span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">h</font></span><a href="funct_3.html#K15">:]</a></span> <a href="binop_1.html#K1">.</a> <font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/><a NAME="E12:4_1"/><b>then </b>
<span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">h</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K15">:]</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="funct_4.html#K2">~</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="funct_4.html#T43">FUNCT_4:43</a>, </i>;<br/><b>hence </b><a NAME="E13:4_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_4.html#K2">~</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">h</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K15">:]</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:4_2"/><i><font color="Green">E40</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">h</font></span><a href="funct_3.html#K15">:]</a></span></span>)</span>
 ;<br/><a NAME="E2:4_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">h</font></span><a href="funct_3.html#K15">:]</a></span>
 <b>by </b><i><a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/><a NAME="E3:4_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">h</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="funct_3.html#D9">FUNCT_3:def 9</a></i>;<br/><a NAME="E4:4_2"/><b>then </b><i><font color="Green">E41</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">h</font> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><a NAME="E5:4_2"/>
<span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">h</font></span><a href="funct_3.html#K15">:]</a></span> <a href="binop_1.html#K1">.</a> <font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/><a NAME="E6:4_2"/><b>then </b><i><font color="Green">E42</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 <b>by </b><i>, <a class="ref" href="funct_3.html#D9">FUNCT_3:def 9</a></i>;<br/><a NAME="E7:4_2"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">z</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">h</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><a NAME="E8:4_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">z</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">h</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K15">:]</a></span>
 <b>by </b><i><a class="ref" href="funct_3.html#D9">FUNCT_3:def 9</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_4.html#K2">~</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">h</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K15">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">z</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> = 
<span class="p1">(<span class="default"><a href="funct_4.html#K2">~</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">h</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K15">:]</a></span> <a href="binop_1.html#K1">.</a> <font color="Maroon">z</font>,<font color="Maroon">y</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="funct_4.html#K2">~</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i>, <a class="ref" href="funct_3.html#D9">FUNCT_3:def 9</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i>, <a class="ref" href="funct_4.html#D2">FUNCT_4:def 2</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">h</font></span><a href="funct_3.html#K15">:]</a></span> <a href="binop_1.html#K1">.</a> <font color="Maroon">y</font>,<font color="Maroon">z</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_3.html#D9">FUNCT_3:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">h</font></span><a href="funct_3.html#K15">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:4"/>
 <a href="funct_4.html#K2">~</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">h</font></span><a href="funct_3.html#K15">:]</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="funct_4.html#K2">~</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1"><a href="funct_3.html#K15">[:</a><span class="default"><font color="Maroon">h</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K15">:]</a></span>
 <b>by </b><i>, <a class="ref" href="funct_4.html#D2">FUNCT_4:def 2</a></i>;<br/>


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