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<b>consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>take </b><font color="Maroon">c<sub>3</sub></font> =  <a href="msualg_3.html#K2" target="_self">id</a> <font color="Maroon">c<sub>2</sub></font>;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="msualg_3.html#D2" target="_self">MSUALG_3:def 2</a><br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/>



<b>assume </b><a NAME="E2:5_1_1"/><i><font color="Green">E3</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/>

<a NAME="E3:5_1_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="msualg_3.html#K2" target="_self">id</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E4:5_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="partfun1.html#K6">id</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="msualg_3.html#E2:5_1_1"><i><font color="Green">E3</font></i></a>, <a class="ref" href="msualg_3.html#D1" target="_self">Def1</a></i>;<br/>
<b>hence </b><a NAME="E5:5_1_1"/>
<font color="Maroon">c<sub>5</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 ;<br/>


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