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<b>let </b><font color="Maroon">A</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">B</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">C</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A</font>,<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="zfmisc_1.html#K2">:]</a></span>, <font color="Maroon">g</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A</font>,<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/>



<b>assume </b><a NAME="E1:6"/><i><font color="Green">E16</font></i>: 
( <span class="p1">(<span class="default"><a href="funct_3.html#K9">pr1</a> <font color="Maroon">B</font>,<font color="Maroon">C</font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="funct_3.html#K9">pr1</a> <font color="Maroon">B</font>,<font color="Maroon">C</font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">g</font> &amp; <span class="p1">(<span class="default"><a href="funct_3.html#K10">pr2</a> <font color="Maroon">B</font>,<font color="Maroon">C</font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="funct_3.html#K10">pr2</a> <font color="Maroon">B</font>,<font color="Maroon">C</font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">g</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font>;<br/><b>consider </b><font color="Maroon">b1</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">B</font>, <font color="Maroon">c1</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font><b> such that </b><br/><a NAME="E2:6_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">c1</font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i><a class="ref" href="domain_1.html#T9">DOMAIN_1:9</a></i>;<br/><b>consider </b><font color="Maroon">b2</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">B</font>, <font color="Maroon">c2</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font><b> such that </b><br/><a NAME="E4:6_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b2</font>,<font color="Maroon">c2</font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i><a class="ref" href="domain_1.html#T9">DOMAIN_1:9</a></i>;<br/><a NAME="E5:6_1"/><i><font color="Green">E33</font></i>: 
( <span class="p1">(<span class="default"><a href="funct_3.html#K9">pr1</a> <font color="Maroon">B</font>,<font color="Maroon">C</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font> &amp; <span class="p1">(<span class="default"><a href="funct_3.html#K9">pr1</a> <font color="Maroon">B</font>,<font color="Maroon">C</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">b2</font>,<font color="Maroon">c2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font> &amp; <span class="p1">(<span class="default"><a href="funct_3.html#K10">pr2</a> <font color="Maroon">B</font>,<font color="Maroon">C</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c1</font> &amp; <span class="p1">(<span class="default"><a href="funct_3.html#K10">pr2</a> <font color="Maroon">B</font>,<font color="Maroon">C</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">b2</font>,<font color="Maroon">c2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c2</font> )
 <b>by </b><i><a class="ref" href="funct_3.html#D5">FUNCT_3:def 5</a>, <a class="ref" href="funct_3.html#D6">FUNCT_3:def 6</a></i>;<br/><a NAME="E6:6_1"/>
( <span class="p1">(<span class="default"><a href="funct_3.html#K9">pr1</a> <font color="Maroon">B</font>,<font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_3.html#K9">pr1</a> <font color="Maroon">B</font>,<font color="Maroon">C</font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> &amp; <span class="p1">(<span class="default"><a href="funct_3.html#K10">pr2</a> <font color="Maroon">B</font>,<font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_3.html#K10">pr2</a> <font color="Maroon">B</font>,<font color="Maroon">C</font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> &amp; <span class="p1">(<span class="default"><a href="funct_3.html#K9">pr1</a> <font color="Maroon">B</font>,<font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_3.html#K9">pr1</a> <font color="Maroon">B</font>,<font color="Maroon">C</font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">g</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> &amp; <span class="p1">(<span class="default"><a href="funct_3.html#K10">pr2</a> <font color="Maroon">B</font>,<font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_3.html#K10">pr2</a> <font color="Maroon">B</font>,<font color="Maroon">C</font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">g</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> )
 <b>by </b><i><a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>;<br/><b>hence </b><a NAME="E7:6_1"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font>
 <b>by </b><i>, , , </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:6"/>
<font color="Maroon">f</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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