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<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="glib_003.html#NM1" title="GLIB_003:NM.1">WGraph</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">G</font> is  <a href="glib_005.html#V1" title="GLIB_005:attr.1">natural-weighted</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_003.html#V8" title="GLIB_003:attr.8">nonnegative-weighted</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:6_1_1"/>
<font color="Maroon" title="c1">G</font> is  <a href="glib_005.html#V1" title="GLIB_005:attr.1">natural-weighted</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">G</font> is  <a href="glib_003.html#V8" title="GLIB_003:attr.8">nonnegative-weighted</a> </span><br/>

<a NAME="E2:6_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E6">A1</font></span>: 
 <a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font> is  <a href="valued_0.html#V4" title="VALUED_0:attr.4">natural-valued</a> 
 
;<br/>
<a NAME="E3:6_1_1"/>
 for <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font></span>)</span> holds <br/><font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_5.html#K8" title="GRAPH_5:func.8">Real&gt;=0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="graph_5.html#D12" onmouseover="rs('graph_5/D12')" onmouseout="rh()">GRAPH_5:def 12</a>, <a class="txt" href="#E2:6_1_1"><span class="lab"><font color="Green" title="E6">A1</font></span></a></span>;<br/>
<a NAME="E4:6_1_1"/><span class="kw">then </span>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_5.html#K8" title="GRAPH_5:func.8">Real&gt;=0</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E5:6_1_1"/>
<font color="Maroon" title="c1">G</font> is  <a href="glib_003.html#V8" title="GLIB_003:attr.8">nonnegative-weighted</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"> verum</span><br/>


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