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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" 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>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_003.html#V7" title="GLIB_003:attr.7">real-weighted</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:75_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" 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#V7" title="GLIB_003:attr.7">real-weighted</a> </span><br/>

<a NAME="E2:75_1_1"/><span class="kw">then </span>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_003.html#D14" target="_self" title="GLIB_003:def.14">Def14</a></span>;<br/>
<a NAME="E3:75_1_1"/><span class="kw">then </span>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">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="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E4:75_1_1"/><span class="kw">then </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#V3" title="VALUED_0:attr.3">real-valued</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_0.html#D3" title="VALUED_0:def.3">VALUED_0:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:75_1_1"/>
<font color="Maroon" title="c1">G</font> is  <a href="glib_003.html#V7" title="GLIB_003:attr.7">real-weighted</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_003.html#D13" target="_self" title="GLIB_003:def.13">Def13</a></span>; <a class="txt" 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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