<?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">E</font>, <font color="Olive" title="b2">V</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">G4</font> being    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c1">G3</font>,<font color="Olive" title="b1">E</font><br/>  for <font color="Olive" title="b4">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="b2">V</font><br/>  for <font color="Olive" title="b5">G2</font> being    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Olive" title="b4">G1</font>,<font color="Olive" title="b1">E</font>  st <font color="Olive" title="b1">E</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="c1">G3</font> holds <br/><font color="Olive" title="b5">G2</font> is    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Olive" title="b3">G4</font>,<font color="Olive" title="b2">V</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">E</font>, <font color="Maroon" title="c3">V</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">  for <font color="Olive" title="b1">G4</font> being    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c1">G3</font>,<font color="Maroon" title="c2">E</font><br/>  for <font color="Olive" title="b2">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="c3">V</font><br/>  for <font color="Olive" title="b3">G2</font> being    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Olive" title="b2">G1</font>,<font color="Maroon" title="c2">E</font>  st <font color="Maroon" title="c2">E</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="c1">G3</font> holds <br/><font color="Olive" title="b3">G2</font> is    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Olive" title="b1">G4</font>,<font color="Maroon" title="c3">V</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">G4</font> be    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c1">G3</font>,<font color="Maroon" title="c2">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">  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="c3">V</font><br/>  for <font color="Olive" title="b2">G2</font> being    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Olive" title="b1">G1</font>,<font color="Maroon" title="c2">E</font>  st <font color="Maroon" title="c2">E</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="c1">G3</font> holds <br/><font color="Olive" title="b2">G2</font> is    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c4">G4</font>,<font color="Maroon" title="c3">V</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">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="c3">V</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">  for <font color="Olive" title="b1">G2</font> being    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c2">E</font>  st <font color="Maroon" title="c2">E</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="c1">G3</font> holds <br/><font color="Olive" title="b1">G2</font> is    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c4">G4</font>,<font color="Maroon" title="c3">V</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">G2</font> be    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c2">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"> ( <font color="Maroon" title="c2">E</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="c1">G3</font> implies <font color="Maroon" title="c6">G2</font> is    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c4">G4</font>,<font color="Maroon" title="c3">V</font> )</span><br/>









<span class="kw">assume </span><a NAME="E1:59"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
<font color="Maroon" title="c2">E</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="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"> <font color="Maroon" title="c6">G2</font> is    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c4">G4</font>,<font color="Maroon" title="c3">V</font></span><br/>

<span class="lab"><font color="Green" title="E30">A2</font></span>:  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c6">G2</font> = 
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c5">G1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T4" onmouseover="rs('glib_007/T4')" onmouseout="rh()">GLIB_007:4</a></span>
<br/>.= 
 <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#T15" target="_self" onmouseover="rs('glib_012/T15')" onmouseout="rh()">Th15</a></span>
<br/>.= 
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c4">G4</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T4" onmouseover="rs('glib_007/T4')" onmouseout="rh()">GLIB_007:4</a></span>
;<br/>
<a NAME="E3:59"/>
 <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> <font color="Maroon" title="c5">G1</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/>
<a NAME="E4:59"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A3</font></span>: 
<font color="Maroon" title="c2">E</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="c5">G1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="xboole_1.html#T1" onmouseover="rs('xboole_1/T1')" onmouseout="rh()">XBOOLE_1:1</a></span>;<br/>
<a NAME="E5:59"/><span class="lab"><font color="Green" title="E32">A4</font></span>: 
<font color="Maroon" title="c6">G2</font> is    <a href="glib_006.html#M1" title="GLIB_006:mode.1">Supergraph</a> of <font color="Maroon" title="c4">G4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="glibpre0.html#T50" onmouseover="rs('glibpre0/T50')" onmouseout="rh()">GLIBPRE0:50</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_2"><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="E1:59_2"/>
( <font color="Maroon" title="c3">V</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="c1">G3</font> or  not <font color="Maroon" title="c3">V</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="c1">G3</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_2_1"><span class="kw">suppose </span></a><a NAME="E1:59_2_1"/><span class="lab"><font color="Green" title="E33">A5</font></span>: 
<font color="Maroon" title="c3">V</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="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"> <font color="Maroon" title="c6">G2</font> is    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c4">G4</font>,<font color="Maroon" title="c3">V</font></span><br/><div class="add"><a NAME="E2:59_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A6</font></span>: 
<font color="Maroon" title="c3">V</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">G4</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T4" onmouseover="rs('glib_007/T4')" onmouseout="rh()">GLIB_007:4</a></span>;<br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="59_2_1_1"><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">D</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  ex <font color="Olive" title="b2">f</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">D</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="c4">G4</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c6">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="c4">G4</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b1">D</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">D</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c6">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="c4">G4</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">f</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c6">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="c4">G4</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">f</font> )</span></a><div class="add"><span class="kw">consider </span><font color="Maroon" title="c7">D</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> , <font color="Maroon" title="c8">f</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="E2:59_2_1_1"/><span class="lab"><font color="Green" title="E35">A7</font></span>: 
( <font color="Maroon" title="c7">D</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="c5">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="c7">D</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">D</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c5">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="c8">f</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c5">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="c8">f</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59_2_1"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <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="c9">D</font> = <font color="Maroon" title="c7">D</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">f</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="c9">D</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="c4">G4</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c6">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="c4">G4</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c9">D</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">D</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c6">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="c4">G4</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">f</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c6">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="c4">G4</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">f</font> )</span><br/><span class="kw">take </span><font color="Maroon" title="c10">f</font> = <font color="Maroon" title="c8">f</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c9">D</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="c4">G4</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c6">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="c4">G4</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c9">D</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c10">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">D</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c10">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c6">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="c4">G4</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c10">f</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c6">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="c4">G4</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c10">f</font> )</span><br/><span class="kw">thus </span><a NAME="E3:59_2_1_1"/>
<font color="Maroon" title="c9">D</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="c4">G4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:59_2_1_1"><span class="lab"><font color="Green" title="E35">A7</font></span></a>, <a class="ref" href="glib_007.html#T4" onmouseover="rs('glib_007/T4')" onmouseout="rh()">GLIB_007:4</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="c6">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="c4">G4</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c9">D</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c10">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">D</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c10">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c6">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="c4">G4</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c10">f</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c6">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="c4">G4</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c10">f</font> )</span><br/><span class="kw">thus </span> <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c6">G2</font> = 
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c5">G1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T4" onmouseover="rs('glib_007/T4')" onmouseout="rh()">GLIB_007:4</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="c4">G4</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c9">D</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:59_2_1_1"><span class="lab"><font color="Green" title="E35">A7</font></span></a>, <a class="ref" href="glib_007.html#T4" onmouseover="rs('glib_007/T4')" onmouseout="rh()">GLIB_007:4</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="c10">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">D</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c10">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c6">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="c4">G4</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c10">f</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c6">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="c4">G4</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c10">f</font> )</span><br/><span class="kw">thus </span><a NAME="E5:59_2_1_1"/>
(  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c10">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">D</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c10">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:59_2_1_1"><span class="lab"><font color="Green" title="E35">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="c6">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="c4">G4</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c10">f</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c6">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="c4">G4</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c10">f</font> )</span><br/><a NAME="E6:59_2_1_1"/>
<font color="Maroon" title="c2">E</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#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">E</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E29">A1</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="E7:59_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A8</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c10">f</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#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">E</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E2:59_2_1_1"><span class="lab"><font color="Green" title="E35">A7</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="E8:59_2_1_1"/><span class="kw">then </span>
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c10">f</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <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="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c2">E</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/><a NAME="E9:59_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A9</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c10">f</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relset_1.html#K1" title="RELSET_1:func.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="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">E</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T61" onmouseover="rs('relat_1/T61')" onmouseout="rh()">RELAT_1:61</a></span>;<br/><a NAME="E10:59_2_1_1"/>
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c10">f</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <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="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c2">E</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:59_2_1_1"><span class="lab"><font color="Green" title="E36">A8</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/><a NAME="E11:59_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A10</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c10">f</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relset_1.html#K1" title="RELSET_1:func.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="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">E</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><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="E39">A11</font></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="c5">G1</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">E</font> = 
<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="c5">G1</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <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></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">E</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="relat_1.html#T74" onmouseover="rs('relat_1/T74')" onmouseout="rh()">RELAT_1:74</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="c1">G3</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">E</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_006.html#T69" onmouseover="rs('glib_006/T69')" onmouseout="rh()">GLIB_006:69</a></span>
;<br/><span class="lab"><font color="Green" title="E40">A12</font></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="c5">G1</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">E</font> = 
<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="c5">G1</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <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></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">E</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="relat_1.html#T74" onmouseover="rs('relat_1/T74')" onmouseout="rh()">RELAT_1:74</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="c1">G3</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">E</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_006.html#T69" onmouseover="rs('glib_006/T69')" onmouseout="rh()">GLIB_006:69</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="c6">G2</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="c5">G1</font></span>)</span> <a href="funct_4.html#K9" title="FUNCT_4:func.9">+*</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="c5">G1</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">E</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:59"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="ref" href="glib_007.html#D1" onmouseover="rs('glib_007/D1')" onmouseout="rh()">GLIB_007:def 1</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="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="c10">f</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<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="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">E</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:59_2_1_1"><span class="lab"><font color="Green" title="E35">A7</font></span></a>, <a class="txt" href="#E13:59_2_1_1"><span class="lab"><font color="Green" title="E40">A12</font></span></a>, <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="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"><span class="p3">(<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="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">E</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c10">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:59_2_1_1"><span class="lab"><font color="Green" title="E38">A10</font></span></a>, <a class="ref" href="funct_4.html#T35" onmouseover="rs('funct_4/T35')" onmouseout="rh()">FUNCT_4:35</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#K9" title="FUNCT_4:func.9">+*</a> <span class="p2">(<span class="default"><span class="p3">(<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="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">E</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c10">f</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="c4">G4</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c10">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="glib_007.html#D1" onmouseover="rs('glib_007/D1')" onmouseout="rh()">GLIB_007:def 1</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#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c6">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="c4">G4</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c10">f</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="c6">G2</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="c5">G1</font></span>)</span> <a href="funct_4.html#K9" title="FUNCT_4:func.9">+*</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="c5">G1</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">E</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:59"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="ref" href="glib_007.html#D1" onmouseover="rs('glib_007/D1')" onmouseout="rh()">GLIB_007:def 1</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="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="c10">f</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<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="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">E</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:59_2_1_1"><span class="lab"><font color="Green" title="E35">A7</font></span></a>, <a class="txt" href="#E12:59_2_1_1"><span class="lab"><font color="Green" title="E39">A11</font></span></a>, <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="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"><span class="p3">(<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="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">E</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c10">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:59_2_1_1"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="ref" href="funct_4.html#T35" onmouseover="rs('funct_4/T35')" onmouseout="rh()">FUNCT_4:35</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#K9" title="FUNCT_4:func.9">+*</a> <span class="p2">(<span class="default"><span class="p3">(<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="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">E</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c10">f</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="c4">G4</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c10">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="glib_007.html#D1" onmouseover="rs('glib_007/D1')" onmouseout="rh()">GLIB_007:def 1</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><span class="kw">hence </span><a NAME="E4:59_2_1"/>
<font color="Maroon" title="c6">G2</font> is    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c4">G4</font>,<font color="Maroon" title="c3">V</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:59"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E5:59"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E2:59_2_1"><span class="lab"><font color="Green" title="E34">A6</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_2_2"><span class="kw">suppose </span></a><a NAME="E1:59_2_2"/>
 not <font color="Maroon" title="c3">V</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="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"> <font color="Maroon" title="c6">G2</font> is    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c4">G4</font>,<font color="Maroon" title="c3">V</font></span><br/><div class="add"><a NAME="E2:59_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A13</font></span>: 
( <font color="Maroon" title="c5">G1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c1">G3</font> &amp;  not <font color="Maroon" title="c3">V</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">G4</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>, <a class="ref" href="glib_007.html#T4" onmouseover="rs('glib_007/T4')" onmouseout="rh()">GLIB_007:4</a></span>;<br/><a NAME="E3:59_2_2"/>
<font color="Maroon" title="c1">G3</font> is    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c4">G4</font>,<font color="Maroon" title="c2">E</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T3" onmouseover="rs('glib_007/T3')" onmouseout="rh()">GLIB_007:3</a></span>;<br/><a NAME="E4:59_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">G1</font> is    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c4">G4</font>,<font color="Maroon" title="c2">E</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:59_2_2"><span class="lab"><font color="Green" title="E33">A13</font></span></a>, <a class="ref" href="glib_007.html#T2" onmouseover="rs('glib_007/T2')" onmouseout="rh()">GLIB_007:2</a></span>;<br/><a NAME="E5:59_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">G4</font> is    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c2">E</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T3" onmouseover="rs('glib_007/T3')" onmouseout="rh()">GLIB_007:3</a></span>;<br/><a NAME="E6:59_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">G2</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c4">G4</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T1" onmouseover="rs('glib_007/T1')" onmouseout="rh()">GLIB_007:1</a></span>;<br/><span class="kw">hence </span><a NAME="E7:59_2_2"/>
<font color="Maroon" title="c6">G2</font> is    <a href="glib_012.html#M1" title="GLIB_012:mode.1">addLoops</a> of <font color="Maroon" title="c4">G4</font>,<font color="Maroon" title="c3">V</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:59"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E2:59_2_2"><span class="lab"><font color="Green" title="E33">A13</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
