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<b>let </b><font color="Maroon">X</font> be    <a href="struct_0.html#L1">1-sorted</a> ;<br/><b>let </b><font color="Maroon">Y</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L1">1-sorted</a> , <font color="Maroon">Z</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">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">X</font>,<font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">Y</font>,<font color="Maroon">Z</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:2"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">f</font> is <a href="funct_2.html#V2">onto</a>
 <b>and </b><br/><a NAME="E2:2"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">g</font> is <a href="funct_2.html#V2">onto</a>
 ;<br/>

 <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> = 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y</font>
<b>by </b><i>, <a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>
<br/>.= 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font>
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>
;<br/>
<b>then </b> <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font></span>)</span> = 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">g</font>
<b>by </b><i><a class="ref" href="relat_1.html#T47">RELAT_1:47</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Z</font>
<b>by </b><i>, <a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>
;<br/>
<b>hence </b><a NAME="E5:2"/>
<font color="Maroon">g</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</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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