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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></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">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be  <a href="funct_1.html#V2">one-to-one</a> <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>







<b>assume </b><a NAME="E1:16"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:16"/>
<font color="Maroon">c<sub>4</sub></font> <a href="partfun2.html#K2" target="_self">"</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="partfun2.html#K2" target="_self">"</a> 
 
;<br/>
<a NAME="E3:16"/><b>then </b><i><font color="Green">E8</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun2.html#K2" target="_self">"</a> </span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="partfun2.html#E1:16"><i><font color="Green">E7</font></i></a>, <a class="ref" href="partfun2.html#T18" target="_self">Th18</a></i>;<br/>
<b>thus </b><a NAME="E4:16"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun2.html#K2" target="_self">"</a> </span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="partfun2.html#E1:16"><i><font color="Green">E7</font></i></a>, <a class="ref" href="partfun2.html#T18" target="_self">Th18</a></i>;<br/>

<a NAME="E5:16"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun2.html#K2" target="_self">"</a> </span>)</span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="partfun2.html#E1:16"><i><font color="Green">E7</font></i></a>, <a class="txt" href="partfun2.html#E3:16"><i><font color="Green">E8</font></i></a>, <a class="ref" href="funct_1.html#T55">FUNCT_1:55</a></i>;<br/>
<b>hence </b><a NAME="E6:16"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun2.html#K2" target="_self">"</a> </span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="partfun2.html#E4:16"><i><font color="Green">E9</font></i></a>, <a class="ref" href="partfun2.html#T9" target="_self">Th9</a></i>;<br/>


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