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<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="funct_1.html#NM1">Function</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="comput_1.html#D6" target="_self">COMPUT_1:def 6</a><br/>

<b>assume </b><a NAME="E1:84_1_1"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span> )
 ;<br/>

<a NAME="E2:84_1_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>;<br/>
<a NAME="E3:84_1_1"/><b>then </b><i><font color="Green">E50</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="comput_1.html#E1:84_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:84_1_1"/>
(  not <font color="Maroon">c<sub>2</sub></font> is <a href="xboole_0.html#V1">empty</a> or <font color="Maroon">c<sub>3</sub></font> is <a href="xboole_0.html#V1">empty</a> or  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <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> )
 ;<br/>

<b>assume </b><a NAME="E5:84_1_1"/>
( not <font color="Maroon">c<sub>2</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp; not <font color="Maroon">c<sub>3</sub></font> is <a href="xboole_0.html#V1">empty</a> )
 ;<br/>

<b>take </b><font color="Maroon">c<sub>4</sub></font> =  <a href="comput_1.html#K3" target="_self">arity</a> <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>take </b>
 <a href="numbers.html#K5">NAT</a> 
;<br/>

<b>thus </b><a NAME="E6:84_1_1"/>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a>  &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a>  )
 <b>by </b><i><a class="txt" href="comput_1.html#E3:84_1_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="comput_1.html#T24" target="_self">Th24</a></i>;<br/>


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