<?xml version="1.0"?>
<div class="add">

<a NAME="E1:67_1_1"/><i><font color="Green">E55</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">w</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">v</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">w</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E2:67_1_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">w</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">v</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">w</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T18">FUNCT_4:18</a></i>;<br/>
<a NAME="E3:67_1_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">w</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E4:67_1_1"/>
<font color="Maroon">v</font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">w</font> is   <a href="sublemma.html#NM1">Val_Sub</a> of <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="sublemma.html#T1" target="_self">Th1</a>, <a class="ref" href="relset_1.html#T11">RELSET_1:11</a></i>;<br/>


</div>
