<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">G3</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</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">  for <font color="Olive" title="b1">V1</font>, <font color="Olive" title="b2">V2</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span><br/>  for <font color="Olive" title="b3">G1</font> being    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c1">G3</font>,<font color="Olive" title="b1">V1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">V2</font>  st <font color="Olive" title="b1">V1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b2">V2</font> holds <br/> ex <font color="Olive" title="b4">G2</font> being    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c1">G3</font>,<font color="Olive" title="b1">V1</font> st <font color="Olive" title="b3">G1</font> is    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Olive" title="b4">G2</font>,<font color="Olive" title="b2">V2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V1</font>, <font color="Maroon" title="c3">V2</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</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">  for <font color="Olive" title="b1">G1</font> being    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c1">G3</font>,<font color="Maroon" title="c2">V1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">V2</font>  st <font color="Maroon" title="c2">V1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c3">V2</font> holds <br/> ex <font color="Olive" title="b2">G2</font> being    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c1">G3</font>,<font color="Maroon" title="c2">V1</font> st <font color="Olive" title="b1">G1</font> is    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Olive" title="b2">G2</font>,<font color="Maroon" title="c3">V2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">G1</font> be    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c1">G3</font>,<font color="Maroon" title="c2">V1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">V2</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">V1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c3">V2</font> implies  ex <font color="Olive" title="b1">G2</font> being    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c1">G3</font>,<font color="Maroon" title="c2">V1</font> st <font color="Maroon" title="c4">G1</font> is    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Olive" title="b1">G2</font>,<font color="Maroon" title="c3">V2</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:48"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
<font color="Maroon" title="c2">V1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c3">V2</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">G2</font> being    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c1">G3</font>,<font color="Maroon" title="c2">V1</font> st <font color="Maroon" title="c4">G1</font> is    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Olive" title="b1">G2</font>,<font color="Maroon" title="c3">V2</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c5">E3</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> , <font color="Maroon" title="c6">f3</font> being   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><br/><a NAME="E3:48"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
( <font color="Maroon" title="c5">E3</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">E3</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c6">f3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">E3</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c6">f3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">V2</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_012.html#D5" target="_self" onmouseover="rs('glib_012/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">E1</font> = <font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">f1</font> = <font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">s1</font> = <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">t1</font> = <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>;<br/>
<a NAME="E4:48"/><span class="lab"><font color="Green" title="E26">A3</font></span>: 
<font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">E3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="relat_1.html#T132" onmouseover="rs('relat_1/T132')" onmouseout="rh()">RELAT_1:132</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E27">A4</font></span>: <font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c5">E3</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T28" onmouseover="rs('xboole_1/T28')" onmouseout="rh()">XBOOLE_1:28</a></span>
<br/>.= 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="relat_1.html#T61" onmouseover="rs('relat_1/T61')" onmouseout="rh()">RELAT_1:61</a></span>
;<br/>
<span class="lab"><font color="Green" title="E28">A5</font></span>:  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" onmouseover="rs('funct_4/D1')" onmouseout="rh()">FUNCT_4:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:48"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>
;<br/>
<span class="lab"><font color="Green" title="E29">A6</font></span>:  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" onmouseover="rs('funct_4/D1')" onmouseout="rh()">FUNCT_4:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:48"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>
;<br/>
<span class="lab"><font color="Green" title="E30">A7</font></span>: <font color="Maroon" title="c2">V1</font> = 
<font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="xboole_1.html#T7" onmouseover="rs('xboole_1/T7')" onmouseout="rh()">XBOOLE_1:7</a>, <a class="ref" href="funct_1.html#T77" onmouseover="rs('funct_1/T77')" onmouseout="rh()">FUNCT_1:77</a></span>
<br/>.= 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T115" onmouseover="rs('relat_1/T115')" onmouseout="rh()">RELAT_1:115</a></span>
;<br/>
<a NAME="E9:48"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A8</font></span>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T12" onmouseover="rs('xboole_1/T12')" onmouseout="rh()">XBOOLE_1:12</a></span>;<br/>
<a NAME="E10:48"/><span class="lab"><font color="Green" title="E32">A9</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T17" onmouseover="rs('funct_4/T17')" onmouseout="rh()">FUNCT_4:17</a></span>;<br/>
<a NAME="E11:48"/>
<span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T9" onmouseover="rs('xboole_1/T9')" onmouseout="rh()">XBOOLE_1:9</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">s1</font> = <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:48"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="txt" href="#E9:48"><span class="lab"><font color="Green" title="E31">A8</font></span></a>, <a class="txt" href="#E10:48"><span class="lab"><font color="Green" title="E32">A9</font></span></a>, <a class="ref" href="xboole_1.html#T1" onmouseover="rs('xboole_1/T1')" onmouseout="rh()">XBOOLE_1:1</a>, <a class="ref" href="funct_2.html#T2" onmouseover="rs('funct_2/T2')" onmouseout="rh()">FUNCT_2:2</a></span>;<br/>
<a NAME="E13:48"/><span class="lab"><font color="Green" title="E33">A10</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T17" onmouseover="rs('funct_4/T17')" onmouseout="rh()">FUNCT_4:17</a></span>;<br/>
<a NAME="E14:48"/>
<span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T9" onmouseover="rs('xboole_1/T9')" onmouseout="rh()">XBOOLE_1:9</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c12">t1</font> = <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:48"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="txt" href="#E9:48"><span class="lab"><font color="Green" title="E31">A8</font></span></a>, <a class="txt" href="#E13:48"><span class="lab"><font color="Green" title="E33">A10</font></span></a>, <a class="ref" href="xboole_1.html#T1" onmouseover="rs('xboole_1/T1')" onmouseout="rh()">XBOOLE_1:1</a>, <a class="ref" href="funct_2.html#T2" onmouseover="rs('funct_2/T2')" onmouseout="rh()">FUNCT_2:2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">G2</font> =  <a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>);<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="48_5"><span class="kw">now </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"> (  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p2">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>)</span>)</span> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p2">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>)</span>)</span> &amp; (  for <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font> holds <br/>( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p3">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p3">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> ) ) )</span></a><div class="add"><span class="kw">thus </span><a NAME="E1:48_5"/>
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p2">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>)</span>)</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"> (  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p2">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>)</span>)</span> &amp; (  for <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font> holds <br/>( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p3">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p3">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> ) ) )</span><br/><span class="kw">thus </span><a NAME="E2:48_5"/>
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p2">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" onmouseover="rs('xboole_1/T7')" onmouseout="rh()">XBOOLE_1:7</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">  for <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font> holds <br/>( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p3">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p3">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c14">e</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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="c14">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font> implies ( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p3">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">e</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p3">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">e</font> ) )</span><br/><span class="kw">assume </span><a NAME="E3:48_5"/><span class="lab"><font color="Green" title="E34">A11</font></span>: 
<font color="Maroon" title="c14">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</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"> ( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p3">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">e</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p3">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">e</font> )</span><br/><a NAME="E4:48_5"/><span class="kw">then </span>
<font color="Maroon" title="c14">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">E3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>;<br/><a NAME="E5:48_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A12</font></span>: 
 not <font color="Maroon" title="c14">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E4:48"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E5:48"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="txt" href="#E3:48_5"><span class="lab"><font color="Green" title="E34">A11</font></span></a>, <a class="ref" href="xboole_0.html#T5" onmouseover="rs('xboole_0/T5')" onmouseout="rh()">XBOOLE_0:5</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">e</font> = 
<font color="Maroon" title="c11">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">e</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:48_5"><span class="lab"><font color="Green" title="E35">A12</font></span></a>, <a class="ref" href="funct_4.html#T11" onmouseover="rs('funct_4/T11')" onmouseout="rh()">FUNCT_4:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p3">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">e</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"> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p3">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">e</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">e</font> = 
<font color="Maroon" title="c12">t1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">e</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:48_5"><span class="lab"><font color="Green" title="E35">A12</font></span></a>, <a class="ref" href="funct_4.html#T11" onmouseover="rs('funct_4/T11')" onmouseout="rh()">FUNCT_4:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p3">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">e</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"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c14">G2</font> =  <a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">t1</font>) as    <a href="glib_006.html#M1" title="GLIB_006:mode.1">Supergraph</a> of <font color="Maroon" title="c1">G3</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_006.html#D9" onmouseover="rs('glib_006/D9')" onmouseout="rh()">GLIB_006:def 9</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="48_6"><span class="kw">now </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"> (  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font> &amp;  ex <font color="Olive" title="b1">E1</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  ex <font color="Olive" title="b2">f1</font> being   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> st <br/>( <font color="Olive" title="b1">E1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b1">E1</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">E1</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b2">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V1</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">f1</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">f1</font> ) )</span></a><div class="add"><span class="kw">thus </span><a NAME="E1:48_6"/>
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</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">E1</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  ex <font color="Olive" title="b2">f1</font> being   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> st <br/>( <font color="Olive" title="b1">E1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b1">E1</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">E1</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b2">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V1</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">f1</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">f1</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c15">E1</font> = <font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font> as    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c16">f1</font> = <font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span> as   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T52" onmouseover="rs('funct_1/T52')" onmouseout="rh()">FUNCT_1:52</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c17">E1</font> = <font color="Maroon" title="c15">E1</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">f1</font> being   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> st <br/>( <font color="Maroon" title="c17">E1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c17">E1</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b1">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">E1</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b1">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V1</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">f1</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">f1</font> )</span><br/><span class="kw">take </span><font color="Maroon" title="c18">f1</font> = <font color="Maroon" title="c16">f1</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="c17">E1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c17">E1</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c18">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">E1</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c18">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V1</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">f1</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">f1</font> )</span><br/><span class="kw">thus </span><a NAME="E4:48_6"/>
<font color="Maroon" title="c17">E1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E4:48"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="ref" href="xboole_1.html#T63" onmouseover="rs('xboole_1/T63')" onmouseout="rh()">XBOOLE_1:63</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"> (  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c17">E1</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c18">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">E1</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c18">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V1</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">f1</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">f1</font> )</span><br/><span class="kw">thus </span><a NAME="E5:48_6"/>
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c17">E1</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"> (  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c18">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">E1</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c18">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V1</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">f1</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">f1</font> )</span><br/><span class="kw">thus </span><a NAME="E6:48_6"/>
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c18">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">E1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:48"><span class="lab"><font color="Green" title="E27">A4</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"> (  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c18">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V1</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">f1</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">f1</font> )</span><br/><span class="kw">thus </span><a NAME="E7:48_6"/>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c18">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:48"><span class="lab"><font color="Green" title="E30">A7</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"> (  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">f1</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">f1</font> )</span><br/><span class="kw">thus </span><a NAME="E8:48_6"/>
 <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">f1</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">  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">f1</font></span><br/><span class="kw">thus </span><a NAME="E9:48_6"/>
 <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c14">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">f1</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"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">G2</font> = <font color="Maroon" title="c14">G2</font> as    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c1">G3</font>,<font color="Maroon" title="c2">V1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_012.html#D5" target="_self" onmouseover="rs('glib_012/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c15">G2</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="c4">G1</font> is    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c15">G2</font>,<font color="Maroon" title="c3">V2</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c16">E2</font> = <font color="Maroon" title="c5">E3</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span>;<br/>
<span class="lab"><font color="Green" title="E34">A13</font></span>:  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c4">G1</font> = 
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G3</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_012.html#D5" target="_self" onmouseover="rs('glib_012/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c15">G2</font>

;<br/>
<span class="lab"><font color="Green" title="E35">A14</font></span>:  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G1</font> = 
<span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">E3</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E4:48"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="ref" href="xboole_1.html#T45" onmouseover="rs('xboole_1/T45')" onmouseout="rh()">XBOOLE_1:45</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">E3</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T4" onmouseover="rs('xboole_1/T4')" onmouseout="rh()">XBOOLE_1:4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">E3</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>

;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="48_9"><span class="kw">now </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"> (  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c15">G2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c4">G1</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c15">G2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G1</font> &amp; (  for <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c15">G2</font> holds <br/>( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> ) ) )</span></a><div class="add"><span class="kw">thus </span><a NAME="E1:48_9"/>
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c15">G2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c4">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:48"><span class="lab"><font color="Green" title="E34">A13</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"> (  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c15">G2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G1</font> &amp; (  for <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c15">G2</font> holds <br/>( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> ) ) )</span><br/><span class="kw">thus </span><a NAME="E2:48_9"/>
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c15">G2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:48"><span class="lab"><font color="Green" title="E35">A14</font></span></a>, <a class="ref" href="xboole_1.html#T7" onmouseover="rs('xboole_1/T7')" onmouseout="rh()">XBOOLE_1:7</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">  for <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c15">G2</font> holds <br/>( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c17">e</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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="c17">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c15">G2</font> implies ( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> ) )</span><br/><a NAME="E3:48_9"/><span class="lab"><font color="Green" title="E36">A15</font></span>: 
<font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E4:48"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="ref" href="xboole_1.html#T63" onmouseover="rs('xboole_1/T63')" onmouseout="rh()">XBOOLE_1:63</a></span>;<br/><span class="kw">assume </span><a NAME="E4:48_9"/>
<font color="Maroon" title="c17">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c15">G2</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"> ( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><a NAME="E5:48_9"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A16</font></span>: 
<font color="Maroon" title="c17">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_9_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:48_9_1"/><span class="kw">then </span>
( <font color="Maroon" title="c17">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font> or <font color="Maroon" title="c17">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_9_1_1"><span class="kw">suppose </span></a><a NAME="E1:48_9_1_1"/><span class="lab"><font color="Green" title="E38">A17</font></span>: 
<font color="Maroon" title="c17">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</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"> ( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><div class="add"><a NAME="E2:48_9_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A18</font></span>: 
 not <font color="Maroon" title="c17">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48_9"><span class="lab"><font color="Green" title="E36">A15</font></span></a>, <a class="txt" href="#E5:48_9"><span class="lab"><font color="Green" title="E37">A16</font></span></a>, <a class="ref" href="xboole_0.html#T5" onmouseover="rs('xboole_0/T5')" onmouseout="rh()">XBOOLE_0:5</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font> = 
<font color="Maroon" title="c11">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font>

<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:48"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="txt" href="#E2:48_9_1_1"><span class="lab"><font color="Green" title="E39">A18</font></span></a>, <a class="ref" href="funct_4.html#T11" onmouseover="rs('funct_4/T11')" onmouseout="rh()">FUNCT_4:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:48_9_1_1"><span class="lab"><font color="Green" title="E38">A17</font></span></a>, <a class="ref" href="glib_006.html#D9" onmouseover="rs('glib_006/D9')" onmouseout="rh()">GLIB_006:def 9</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"> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font> = 
<font color="Maroon" title="c12">t1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font>

<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:48"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="txt" href="#E2:48_9_1_1"><span class="lab"><font color="Green" title="E39">A18</font></span></a>, <a class="ref" href="funct_4.html#T11" onmouseover="rs('funct_4/T11')" onmouseout="rh()">FUNCT_4:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:48_9_1_1"><span class="lab"><font color="Green" title="E38">A17</font></span></a>, <a class="ref" href="glib_006.html#D9" onmouseover="rs('glib_006/D9')" onmouseout="rh()">GLIB_006:def 9</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_9_1_2"><span class="kw">suppose </span></a><a NAME="E1:48_9_1_2"/><span class="lab"><font color="Green" title="E38">A19</font></span>: 
<font color="Maroon" title="c17">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</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"> ( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><div class="add"><span class="kw">thus </span><span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font> = 
<font color="Maroon" title="c11">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:48"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="txt" href="#E1:48_9_1_2"><span class="lab"><font color="Green" title="E38">A19</font></span></a>, <a class="ref" href="funct_4.html#T13" onmouseover="rs('funct_4/T13')" onmouseout="rh()">FUNCT_4:13</a></span>
<br/>.= 
<font color="Maroon" title="c6">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:48_9_1_2"><span class="lab"><font color="Green" title="E38">A19</font></span></a>, <a class="ref" href="funct_1.html#T49" onmouseover="rs('funct_1/T49')" onmouseout="rh()">FUNCT_1:49</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E4:48"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E1:48_9_1_2"><span class="lab"><font color="Green" title="E38">A19</font></span></a>, <a class="ref" href="funct_4.html#T13" onmouseover="rs('funct_4/T13')" onmouseout="rh()">FUNCT_4:13</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"> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font> = 
<font color="Maroon" title="c12">t1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:48"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="txt" href="#E1:48_9_1_2"><span class="lab"><font color="Green" title="E38">A19</font></span></a>, <a class="ref" href="funct_4.html#T13" onmouseover="rs('funct_4/T13')" onmouseout="rh()">FUNCT_4:13</a></span>
<br/>.= 
<font color="Maroon" title="c6">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:48_9_1_2"><span class="lab"><font color="Green" title="E38">A19</font></span></a>, <a class="ref" href="funct_1.html#T49" onmouseover="rs('funct_1/T49')" onmouseout="rh()">FUNCT_1:49</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">e</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E4:48"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E1:48_9_1_2"><span class="lab"><font color="Green" title="E38">A19</font></span></a>, <a class="ref" href="funct_4.html#T13" onmouseover="rs('funct_4/T13')" onmouseout="rh()">FUNCT_4:13</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<a NAME="E23:48"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A20</font></span>: 
<font color="Maroon" title="c4">G1</font> is    <a href="glib_006.html#M1" title="GLIB_006:mode.1">Supergraph</a> of <font color="Maroon" title="c15">G2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_006.html#D9" onmouseover="rs('glib_006/D9')" onmouseout="rh()">GLIB_006:def 9</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="48_10"><span class="kw">now </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">  ex <font color="Olive" title="b1">E2</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  ex <font color="Olive" title="b2">f2</font> being   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> st <br/>( <font color="Olive" title="b1">E2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c15">G2</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b1">E2</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">E2</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b2">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V2</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">f2</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">f2</font> )</span></a><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c17">E2</font> = <font color="Maroon" title="c5">E3</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span> as    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c18">f2</font> = <font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c17">E2</font> as   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T52" onmouseover="rs('funct_1/T52')" onmouseout="rh()">FUNCT_1:52</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c19">E2</font> = <font color="Maroon" title="c17">E2</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">f2</font> being   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> st <br/>( <font color="Maroon" title="c19">E2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c15">G2</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c19">E2</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b1">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">E2</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b1">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V2</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">f2</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">f2</font> )</span><br/><span class="kw">take </span><font color="Maroon" title="c20">f2</font> = <font color="Maroon" title="c18">f2</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="c19">E2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c15">G2</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c19">E2</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c20">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">E2</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c20">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V2</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c20">f2</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c20">f2</font> )</span><br/><a NAME="E3:48_10"/>
<font color="Maroon" title="c19">E2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c5">E3</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c19">E2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T79" onmouseover="rs('xboole_1/T79')" onmouseout="rh()">XBOOLE_1:79</a></span>;<br/><a NAME="E4:48_10"/><span class="kw">then </span>
<font color="Maroon" title="c19">E2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c5">E3</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T48" onmouseover="rs('xboole_1/T48')" onmouseout="rh()">XBOOLE_1:48</a></span>;<br/><a NAME="E5:48_10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A22</font></span>: 
<font color="Maroon" title="c19">E2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:48"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="ref" href="xboole_1.html#T28" onmouseover="rs('xboole_1/T28')" onmouseout="rh()">XBOOLE_1:28</a></span>;<br/><a NAME="E6:48_10"/>
<font color="Maroon" title="c19">E2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="xboole_1.html#T63" onmouseover="rs('xboole_1/T63')" onmouseout="rh()">XBOOLE_1:63</a></span>;<br/><a NAME="E7:48_10"/><span class="kw">then </span>
<font color="Maroon" title="c19">E2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:48_10"><span class="lab"><font color="Green" title="E37">A22</font></span></a>, <a class="ref" href="xboole_1.html#T70" onmouseover="rs('xboole_1/T70')" onmouseout="rh()">XBOOLE_1:70</a></span>;<br/><span class="kw">hence </span><a NAME="E8:48_10"/>
<font color="Maroon" title="c19">E2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c15">G2</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"> (  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c19">E2</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c20">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">E2</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c20">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V2</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c20">f2</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c20">f2</font> )</span><br/><span class="kw">thus </span><a NAME="E9:48_10"/>
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c19">E2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:48"><span class="lab"><font color="Green" title="E35">A14</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"> (  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c20">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">E2</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c20">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V2</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c20">f2</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c20">f2</font> )</span><br/><span class="lab"><font color="Green" title="E38">A23</font></span>: <font color="Maroon" title="c19">E2</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">V1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">V2</font></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="relat_1.html#T134" onmouseover="rs('relat_1/T134')" onmouseout="rh()">RELAT_1:134</a></span>
<br/>.= 
<font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">V1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">V2</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c2">V1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T69" onmouseover="rs('funct_1/T69')" onmouseout="rh()">FUNCT_1:69</a></span>
<br/>.= 
<font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c3">V2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:48"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="xboole_1.html#T88" onmouseover="rs('xboole_1/T88')" onmouseout="rh()">XBOOLE_1:88</a></span>
;<br/><span class="kw">thus </span> <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c20">f2</font> = 
<span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c3">V2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:48_10"><span class="lab"><font color="Green" title="E38">A23</font></span></a>, <a class="ref" href="relat_1.html#T61" onmouseover="rs('relat_1/T61')" onmouseout="rh()">RELAT_1:61</a></span>
<br/>.= 
<font color="Maroon" title="c19">E2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E10:48_10"><span class="lab"><font color="Green" title="E38">A23</font></span></a>, <a class="ref" href="xboole_1.html#T28" onmouseover="rs('xboole_1/T28')" onmouseout="rh()">XBOOLE_1:28</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"> (  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c20">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V2</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c20">f2</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c20">f2</font> )</span><br/><span class="kw">thus </span> <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c20">f2</font> = 
<font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c3">V2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:48_10"><span class="lab"><font color="Green" title="E38">A23</font></span></a>, <a class="ref" href="relat_1.html#T115" onmouseover="rs('relat_1/T115')" onmouseout="rh()">RELAT_1:115</a></span>
<br/>.= 
<font color="Maroon" title="c3">V2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="xboole_1.html#T7" onmouseover="rs('xboole_1/T7')" onmouseout="rh()">XBOOLE_1:7</a>, <a class="ref" href="funct_1.html#T77" onmouseover="rs('funct_1/T77')" onmouseout="rh()">FUNCT_1:77</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"> (  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c20">f2</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c20">f2</font> )</span><br/><a NAME="E13:48_10"/><span class="lab"><font color="Green" title="E39">A24</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c6">f3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c19">E2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E4:48"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="ref" href="xboole_1.html#T45" onmouseover="rs('xboole_1/T45')" onmouseout="rh()">XBOOLE_1:45</a></span>;<br/><span class="kw">thus </span> <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c4">G1</font> = 
<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c19">E2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E13:48_10"><span class="lab"><font color="Green" title="E39">A24</font></span></a>, <a class="ref" href="funct_4.html#T70" onmouseover="rs('funct_4/T70')" onmouseout="rh()">FUNCT_4:70</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c20">f2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T14" onmouseover="rs('funct_4/T14')" onmouseout="rh()">FUNCT_4:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c20">f2</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">  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c20">f2</font></span><br/><span class="kw">thus </span> <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c4">G1</font> = 
<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c20">f2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E13:48_10"><span class="lab"><font color="Green" title="E39">A24</font></span></a>, <a class="ref" href="funct_4.html#T70" onmouseover="rs('funct_4/T70')" onmouseout="rh()">FUNCT_4:70</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G3</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f3</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c20">f2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T14" onmouseover="rs('funct_4/T14')" onmouseout="rh()">FUNCT_4:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c15">G2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c20">f2</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"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E25:48"/>
<font color="Maroon" title="c4">G1</font> is    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c15">G2</font>,<font color="Maroon" title="c3">V2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:48"><span class="lab"><font color="Green" title="E34">A13</font></span></a>, <a class="txt" href="#E23:48"><span class="lab"><font color="Green" title="E36">A20</font></span></a>, <a class="ref" href="glib_012.html#D5" target="_self" onmouseover="rs('glib_012/D5')" onmouseout="rh()">Def5</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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