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<b>let </b><font color="Maroon">V</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">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="ens_1.html#K2" target="_self">Maps</a> <font color="Maroon">V</font>;<br/>



<b>consider </b><font color="Maroon">f</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="ens_1.html#K1" target="_self">Funcs</a> <font color="Maroon">V</font>, <font color="Maroon">A</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">V</font>, <font color="Maroon">B</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E2:15"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="domain_1.html#K1">]</a></span>,<font color="Maroon">f</font></span><a href="domain_1.html#K1">]</a></span>
 <b>and </b><br/><a NAME="E3:15"/>
( ( <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) &amp; <font color="Maroon">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font> )
 <b>by </b><i/>;<br/>
<a NAME="E4:15"/>
(  <a href="ens_1.html#K3" target="_self">dom</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K1">`1</a>  &amp;  <a href="ens_1.html#K4" target="_self">cod</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K2">`2</a>  &amp; <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <a href="mcart_1.html#K1">`1</a>  )
 
<b>by </b><i>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<a NAME="E5:15"/><b>then </b>
( <font color="Maroon">m</font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="ens_1.html#K3" target="_self">dom</a> <font color="Maroon">m</font></span>)</span>,<span class="p2">(<span class="default"><a href="ens_1.html#K4" target="_self">cod</a> <font color="Maroon">m</font></span>)</span></span><a href="domain_1.html#K1">]</a></span> &amp; <font color="Maroon">m</font> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <a href="mcart_1.html#K2">`2</a>  )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T8">MCART_1:8</a></i>;<br/>
<b>hence </b><a NAME="E6:15"/>
<font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><span class="p3">(<span class="default"><a href="ens_1.html#K3" target="_self">dom</a> <font color="Maroon">m</font></span>)</span>,<span class="p3">(<span class="default"><a href="ens_1.html#K4" target="_self">cod</a> <font color="Maroon">m</font></span>)</span></span><a href="domain_1.html#K1">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i>, <a class="ref" href="mcart_1.html#T8">MCART_1:8</a></i>;<br/>


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