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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/>



<a NAME="E1:93"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  implies  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="funct_6.html#K9" target="_self">Funcs</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>, <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="card_3.html#K4">product</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wellord2.html#R2">are_equipotent</a>  )
 
<b>by </b><i><a class="txt" href="funct_6.html#E91"><i><font color="Green">Lemma49</font></i></a></i>;<br/>
<i><font color="Green">E53</font></i>:  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="funct_6.html#K9" target="_self">Funcs</a> <a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">c<sub>2</sub></font></span>)</span> = 
 <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="funct_6.html#T78" target="_self">Th78</a></i>
<br/>.= 
 <a href="funct_2.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="card_3.html#T20">CARD_3:20</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <a href="xboole_0.html#K1">{}</a> </span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="funct_5.html#T66">FUNCT_5:66</a></i>
;<br/>
<a NAME="E3:93"/><i><font color="Green">E54</font></i>: 
 <a href="funct_2.html#K1">Funcs</a> <a href="xboole_0.html#K1">{}</a> ,<span class="p1">(<span class="default"><a href="card_3.html#K4">product</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="funct_5.html#T64">FUNCT_5:64</a></i>;<br/>
<a NAME="E4:93"/>
(  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="funct_6.html#K9" target="_self">Funcs</a> <font color="Maroon">c<sub>1</sub></font>,<a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> &amp;  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="card_3.html#K4">product</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funcop_1.html#K2">--&gt;</a> <a href="xboole_0.html#K1">{}</a> </span>)</span></span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="funct_6.html#T79" target="_self">Th79</a>, <a class="ref" href="card_3.html#T19">CARD_3:19</a>, <a class="ref" href="funct_5.html#T66">FUNCT_5:66</a></i>;<br/>
<b>hence </b><a NAME="E5:93"/>
 <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="funct_6.html#K9" target="_self">Funcs</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>, <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="card_3.html#K4">product</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wellord2.html#R2">are_equipotent</a> 
 <b>by </b><i><a class="txt" href="funct_6.html#E1:93"><i><font color="Green">E52</font></i></a>, <a class="txt" href="funct_6.html#E2:93"><i><font color="Green">E53</font></i></a>, <a class="txt" href="funct_6.html#E3:93"><i><font color="Green">E54</font></i></a>, <a class="ref" href="card_1.html#T48">CARD_1:48</a></i>;<br/>


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