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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">R</font> is  <a href="valued_0.html#V4" title="VALUED_0:attr.4">natural-valued</a>  implies <font color="Maroon" title="c1">R</font> is  <a href="counters.html#V3" title="COUNTERS:attr.3">ext-natural-valued</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:54_2_1"/>
<font color="Maroon" title="c1">R</font> is  <a href="valued_0.html#V4" title="VALUED_0:attr.4">natural-valued</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">R</font> is  <a href="counters.html#V3" title="COUNTERS:attr.3">ext-natural-valued</a> </span><br/>

<a NAME="E2:54_2_1"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">rng</a> <font color="Maroon" title="c1">R</font> <a href="xboole_0.html#R2" title="XBOOLE_0:pred.2">c&lt;</a>  <a href="counters.html#K1" title="COUNTERS:func.1">ExtNAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="counters.html#T1" target="_self" onmouseover="rs('counters/T1')" onmouseout="rh()">Th1</a>, <a class="ref" href="valued_0.html#D6" onmouseover="rs('valued_0/D6')" onmouseout="rh()">VALUED_0:def 6</a>, <a class="ref" href="xboole_1.html#T59" onmouseover="rs('xboole_1/T59')" onmouseout="rh()">XBOOLE_1:59</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:54_2_1"/>
<font color="Maroon" title="c1">R</font> is  <a href="counters.html#V3" title="COUNTERS:attr.3">ext-natural-valued</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D8" onmouseover="rs('xboole_0/D8')" onmouseout="rh()">XBOOLE_0:def 8</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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