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

<b>let </b><font color="Maroon" title="c1">R</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">R</font> is <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a> implies <font color="Maroon" title="c1">R</font> is <a href="valued_0.html#V2" title="VALUED_0:attr.2">ext-real-valued</a> )</span><br/>

<b>assume </b><a NAME="E1:2_4_1"/>
 <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c1">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="valued_0.html#D3" target="_self" title="VALUED_0:def.3">VALUED_0:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">R</font> is <a href="valued_0.html#V2" title="VALUED_0:attr.2">ext-real-valued</a></span><br/>

<b>hence </b><a NAME="E2:2_4_1"/>
 <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c1">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K7" title="NUMBERS:func.7">ExtREAL</a> 
 <b>by </b><i><a class="ref" href="numbers.html#T31" title="NUMBERS:th.31">NUMBERS:31</a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="valued_0.html#D2" target="_self" title="VALUED_0:def.2">VALUED_0:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
