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<span class="kw">let </span><font color="Maroon" title="c1">F</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"> ( <font color="Maroon" title="c1">F</font> is  <a href="glib_000.html#V16" title="GLIB_000:attr.16">_trivial</a>  &amp; <font color="Maroon" title="c1">F</font> is  <a href="glib_000.html#V19" title="GLIB_000:attr.19">non-Dmulti</a>  &amp; <font color="Maroon" title="c1">F</font> is  <a href="glib_012.html#V2" title="GLIB_012:attr.2">loopfull</a>  implies <font color="Maroon" title="c1">F</font> is  <a href="glpacy00.html#V5" title="GLPACY00:attr.5">Cycle-like</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:76_2_1"/><span class="lab"><font color="Green" title="E44">A1</font></span>: 
( <font color="Maroon" title="c1">F</font> is  <a href="glib_000.html#V16" title="GLIB_000:attr.16">_trivial</a>  &amp; <font color="Maroon" title="c1">F</font> is  <a href="glib_000.html#V19" title="GLIB_000:attr.19">non-Dmulti</a>  &amp; <font color="Maroon" title="c1">F</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"> <font color="Maroon" title="c1">F</font> is  <a href="glpacy00.html#V5" title="GLPACY00:attr.5">Cycle-like</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="glpacy00.html#D7" target="_self" onmouseover="rs('glpacy00/D7')" onmouseout="rh()">GLPACY00:def 7</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">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> implies  ex <font color="Olive" title="b1">G</font> being   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> st <br/>( <font color="Maroon" title="c1">F</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="Olive" title="b1">G</font> &amp; <font color="Olive" title="b1">G</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a>  ) )</span><br/>

<span class="kw">assume </span><a NAME="E2:76_2_1"/><span class="lab"><font color="Green" title="E45">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">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">  ex <font color="Olive" title="b1">G</font> being   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> st <br/>( <font color="Maroon" title="c1">F</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="Olive" title="b1">G</font> &amp; <font color="Olive" title="b1">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">G1</font> being   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a><span class="kw"> such that </span><br/><a NAME="E4:76_2_1"/><span class="lab"><font color="Green" title="E46">A3</font></span>: 
( <font color="Maroon" title="c3">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c3">G1</font> is  <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:76_2_1"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="ref" href="glib_000.html#D60" onmouseover="rs('glib_000/D60')" onmouseout="rh()">GLIB_000:def 60</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">G2</font> being   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a><span class="kw"> such that </span><br/><a NAME="E6:76_2_1"/><span class="lab"><font color="Green" title="E47">A4</font></span>: 
( <font color="Maroon" title="c4">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c4">G2</font> is  <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:76_2_1"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="txt" href="#E2:76_2_1"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="ref" href="glib_000.html#D63" onmouseover="rs('glib_000/D63')" onmouseout="rh()">GLIB_000:def 63</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">G3</font> being   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a><span class="kw"> such that </span><br/><a NAME="E8:76_2_1"/><span class="lab"><font color="Green" title="E48">A5</font></span>: 
( <font color="Maroon" title="c5">G3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c5">G3</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="#E1:76_2_1"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="txt" href="#E2:76_2_1"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="ref" href="glib_012.html#D2" onmouseover="rs('glib_012/D2')" onmouseout="rh()">GLIB_012:def 2</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c3">G1</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="c1">F</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">G1</font> &amp; <font color="Maroon" title="c3">G1</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E9:76_2_1"/>
( <font color="Maroon" title="c1">F</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">G1</font> &amp; <font color="Maroon" title="c3">G1</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="#E4:76_2_1"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="txt" href="#E6:76_2_1"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="txt" href="#E8:76_2_1"><span class="lab"><font color="Green" title="E48">A5</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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