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<span class="kw">let </span><font color="Maroon" title="c2">G</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="glpacy00.html#D10" target="_self" onmouseover="rs('glpacy00/D10')" onmouseout="rh()">GLPACY00:def 10</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="c2">G</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c1">F</font> implies <font color="Maroon" title="c2">G</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:85_1_1"/>
<font color="Maroon" title="c2">G</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c1">F</font>
 ; <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="c2">G</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:85_1_1"/><span class="lab"><font color="Green" title="E45">A1</font></span>: 
( <font color="Maroon" title="c3">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">F</font> &amp; <font color="Maroon" title="c1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">G0</font> being   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a><span class="kw"> such that </span><br/><a NAME="E5:85_1_1"/><span class="lab"><font color="Green" title="E46">A2</font></span>: 
( <font color="Maroon" title="c1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G0</font> &amp; <font color="Maroon" title="c4">G0</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:85_1_1"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="ref" href="glpacy00.html#D7" target="_self" onmouseover="rs('glpacy00/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<span class="kw">thus </span><a NAME="E6:85_1_1"/>
<font color="Maroon" title="c2">G</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:85_1_1"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="txt" href="#E5:85_1_1"><span class="lab"><font color="Green" title="E46">A2</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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