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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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">R</font> is  <a href="valued_0.html#V6" title="VALUED_0:attr.6">natural-valued</a>  implies <font color="Maroon" title="c1">R</font> is  <a href="partfun3.html#V4" title="PARTFUN3:attr.4">nonnegative-yielding</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:99_1_1"/>
<font color="Maroon" title="c1">R</font> is  <a href="valued_0.html#V6" title="VALUED_0:attr.6">natural-valued</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">R</font> is  <a href="partfun3.html#V4" title="PARTFUN3:attr.4">nonnegative-yielding</a> </span><br/>

<a NAME="E2:99_1_1"/><span class="kw">then </span>
for <font color="Olive" title="b1">r</font> being  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Olive" title="b1">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c1">R</font> holds <br/><font color="Olive" title="b1">r</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E3:99_1_1"/>
<font color="Maroon" title="c1">R</font> is  <a href="partfun3.html#V4" title="PARTFUN3:attr.4">nonnegative-yielding</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun3.html#D4" title="PARTFUN3:def.4">PARTFUN3:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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