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<b>let </b><font color="Maroon">A</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">B</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">A1</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">A2</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">f1</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A1</font>,<font color="Maroon">B</font>;<br/><b>let </b><font color="Maroon">f2</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A2</font>,<font color="Maroon">B</font>;<br/>











<b>assume </b><a NAME="E1:9"/>
<font color="Maroon">f1</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A2</font></span>)</span>
 ;<br/>

<a NAME="E2:9"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="tmap_1.html#K1" target="_self">union</a> <font color="Maroon">f2</font></span>)</span> <a href="partfun1.html#K2">|</a> <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="tmap_1.html#K1" target="_self">union</a> <font color="Maroon">f2</font></span>)</span> <a href="partfun1.html#K2">|</a> <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:9"/>
<font color="Maroon">f1</font> <a href="tmap_1.html#K1" target="_self">union</a> <font color="Maroon">f2</font> <a href="funct_2.html#R1">=</a> <font color="Maroon">f2</font> <a href="tmap_1.html#K1" target="_self">union</a> <font color="Maroon">f1</font>
 <b>by </b><i/>;<br/>


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