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<b>let </b><font color="Maroon">L1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L1">1-sorted</a> , <font color="Maroon">L2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L1">1-sorted</a> ;<br/><b>let </b><font color="Maroon">g1</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">L1</font>,<font color="Maroon">L2</font>;<br/><b>let </b><font color="Maroon">g2</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">L2</font>,<font color="Maroon">L1</font>;<br/>





<b>assume </b><a NAME="E1:42"/>
<font color="Maroon">g2</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">g1</font> <a href="funct_2.html#R2">=</a>  <a href="grcat_1.html#K7">id</a> <font color="Maroon">L1</font>
 ;<br/>

<a NAME="E2:42"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">g2</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">g1</font> <a href="funct_2.html#R2">=</a>  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font>
 
<b>by </b><i><a class="ref" href="grcat_1.html#D11">GRCAT_1:def 11</a></i>;<br/>
<b>hence </b><a NAME="E3:42"/>
<font color="Maroon">g1</font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>by </b><i><a class="ref" href="funct_2.html#T29">FUNCT_2:29</a></i>;<br/>

<a NAME="E4:42"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">g2</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font>
 
<b>by </b><i><a class="txt" href="waybel_1.html#E2:42"><i><font color="Green">E32</font></i></a>, <a class="ref" href="funct_2.html#T29">FUNCT_2:29</a></i>;<br/>
<b>hence </b><a NAME="E5:42"/>
<font color="Maroon">g2</font> is <a href="funct_2.html#V2">onto</a>
 <b>by </b><i><a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/>


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