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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="E1:53"/><i><font color="Green">E33</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_6.html#K6" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="funct_6.html#K6" target="_self">:&gt;</a></span> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="funct_6.html#K3" target="_self">rngs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_6.html#T49" target="_self">Th49</a></i>;<br/>
<b>assume </b><a NAME="E2:53"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_6.html#K6" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="funct_6.html#K6" target="_self">:&gt;</a></span>
 ;<br/>

<a NAME="E3:53"/><b>then </b>
<span class="p1"><a href="funct_6.html#K6" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="funct_6.html#K6" target="_self">:&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_6.html#K6" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="funct_6.html#K6" target="_self">:&gt;</a></span>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E4:53"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="funct_1.html#NM1">Function</a> st <br/>( <span class="p1"><a href="funct_6.html#K6" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="funct_6.html#K6" target="_self">:&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="funct_6.html#K3" target="_self">rngs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; ( for <font color="Olive">b<sub>2</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>2</sub></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_6.html#K3" target="_self">rngs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="funct_6.html#K3" target="_self">rngs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>2</sub></font> ) )
 
<b>by </b><i><a class="txt" href="funct_6.html#E1:53"><i><font color="Green">E33</font></i></a>, <a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/>
<b>hence </b><a NAME="E5:53"/>
<span class="p1"><a href="funct_6.html#K6" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="funct_6.html#K6" target="_self">:&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> is   <a href="funct_1.html#NM1">Function</a>
 ;<br/>


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