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<span class="kw">let </span><font color="Maroon" title="c1">GF</font> be   <a href="glib_000.html#V12" title="GLIB_000:attr.12">Graph-yielding</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</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"> (  not <font color="Maroon" title="c1">GF</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <font color="Maroon" title="c1">GF</font> is  <a href="glib_012.html#V2" title="GLIB_012:attr.2">loopfull</a>  implies  not <font color="Maroon" title="c1">GF</font> is  <a href="glib_000.html#V15" title="GLIB_000:attr.15">loopless</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:31_2_1"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
(  not <font color="Maroon" title="c1">GF</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <font color="Maroon" title="c1">GF</font> is  <a href="glib_012.html#V2" title="GLIB_012:attr.2">loopfull</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">  not <font color="Maroon" title="c1">GF</font> is  <a href="glib_000.html#V15" title="GLIB_000:attr.15">loopless</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:31_2_1"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">GF</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D1" onmouseover="rs('xboole_0/D1')" onmouseout="rh()">XBOOLE_0:def 1</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c3">G</font> being   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a><span class="kw"> such that </span><br/><a NAME="E5:31_2_1"/><span class="lab"><font color="Green" title="E20">A3</font></span>: 
( <font color="Maroon" title="c1">GF</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">G</font> &amp; <font color="Maroon" title="c3">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31_2_1"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E3:31_2_1"><span class="lab"><font color="Green" title="E19">A2</font></span></a></span>;<br/>
<span class="kw">thus </span><a NAME="E6:31_2_1"/>
 not <font color="Maroon" title="c1">GF</font> is  <a href="glib_000.html#V15" title="GLIB_000:attr.15">loopless</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31_2_1"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E3:31_2_1"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="txt" href="#E5:31_2_1"><span class="lab"><font color="Green" title="E20">A3</font></span></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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