<?xml version="1.0"?>
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<span class="kw">let </span><font color="Maroon" title="c1">G2</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">v</font>, <font color="Olive" title="b2">v1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <br/>  for <font color="Olive" title="b3">G1</font> being    <a href="glib_007.html#M4" title="GLIB_007:mode.4">addAdjVertexAll</a> of <font color="Maroon" title="c1">G2</font>,<font color="Olive" title="b1">v</font>,<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b2">v1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>  st <font color="Olive" title="b2">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G2</font> &amp;  not <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G2</font> holds <br/> ex <font color="Olive" title="b4">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>(  not <font color="Olive" title="b4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> &amp; ( <font color="Olive" title="b3">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Olive" title="b1">v</font>,<font color="Olive" title="b4">e</font>,<font color="Olive" title="b2">v1</font> or <font color="Olive" title="b3">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Olive" title="b2">v1</font>,<font color="Olive" title="b4">e</font>,<font color="Olive" title="b1">v</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">v</font>, <font color="Maroon" title="c3">v1</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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">G1</font> being    <a href="glib_007.html#M4" title="GLIB_007:mode.4">addAdjVertexAll</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">v</font>,<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">v1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>  st <font color="Maroon" title="c3">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G2</font> &amp;  not <font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G2</font> holds <br/> ex <font color="Olive" title="b2">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>(  not <font color="Olive" title="b2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> &amp; ( <font color="Olive" title="b1">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">v</font>,<font color="Olive" title="b2">e</font>,<font color="Maroon" title="c3">v1</font> or <font color="Olive" title="b1">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c3">v1</font>,<font color="Olive" title="b2">e</font>,<font color="Maroon" title="c2">v</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">G1</font> be    <a href="glib_007.html#M4" title="GLIB_007:mode.4">addAdjVertexAll</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">v</font>,<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">v1</font></span><a href="tarski.html#K1" title="TARSKI:func.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"> ( <font color="Maroon" title="c3">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G2</font> &amp;  not <font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G2</font> implies  ex <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>(  not <font color="Olive" title="b1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> &amp; ( <font color="Maroon" title="c4">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">v</font>,<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c3">v1</font> or <font color="Maroon" title="c4">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c3">v1</font>,<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c2">v</font> ) ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:87"/><span class="lab"><font color="Green" title="E56">A1</font></span>: 
( <font color="Maroon" title="c3">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G2</font> &amp;  not <font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">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">  ex <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>(  not <font color="Olive" title="b1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> &amp; ( <font color="Maroon" title="c4">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">v</font>,<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c3">v1</font> or <font color="Maroon" title="c4">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c3">v1</font>,<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c2">v</font> ) )</span><br/>

<a NAME="E2:87"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A2</font></span>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">v1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <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">G2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T31" onmouseover="rs('zfmisc_1/T31')" onmouseout="rh()">ZFMISC_1:31</a></span>;<br/>
<a NAME="E3:87"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A3</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="hidden.html#R1" title="HIDDEN:pred.1">=</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">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">v</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="ref" href="glib_007.html#D4" target="_self" onmouseover="rs('glib_007/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">E</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <span class="kw"> such that </span><br/><a NAME="E5:87"/><span class="lab"><font color="Green" title="E59">A4</font></span>: 
(  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">v1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c5">E</font> &amp; <font color="Maroon" title="c5">E</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">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="c1">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">E</font> )
 <span class="kw">and </span><br/><a NAME="E6:87"/><span class="lab"><font color="Green" title="E60">A5</font></span>: 
 for <font color="Olive" title="b1">v2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">v2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">v1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/> ex <font color="Olive" title="b2">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b2">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">E</font> &amp; <font color="Olive" title="b2">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v2</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> &amp; (  for <font color="Olive" title="b3">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b3">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v2</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> holds <br/><font color="Olive" title="b2">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">e2</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="txt" href="#E2:87"><span class="lab"><font color="Green" title="E57">A2</font></span></a>, <a class="ref" href="glib_007.html#D4" target="_self" onmouseover="rs('glib_007/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<a NAME="E7:87"/>
<font color="Maroon" title="c3">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">v1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E9:87"/><span class="lab"><font color="Green" title="E61">A6</font></span>: 
( <font color="Maroon" title="c6">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">E</font> &amp; <font color="Maroon" title="c6">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> )
 <span class="kw">and </span><br/><a NAME="E10:87"/>
 for <font color="Olive" title="b1">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> holds <br/><font color="Maroon" title="c6">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:87"><span class="lab"><font color="Green" title="E60">A5</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c6">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"> (  not <font color="Maroon" title="c6">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> &amp; ( <font color="Maroon" title="c4">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c3">v1</font> or <font color="Maroon" title="c4">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c2">v</font> ) )</span><br/>

<a NAME="E11:87"/>
<font color="Maroon" title="c5">E</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</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">G2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:87"><span class="lab"><font color="Green" title="E59">A4</font></span></a>, <a class="ref" href="xboole_0.html#D7" onmouseover="rs('xboole_0/D7')" onmouseout="rh()">XBOOLE_0:def 7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:87"/><span class="lab"><font color="Green" title="E62">A7</font></span>: 
 not <font color="Maroon" title="c6">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:87"><span class="lab"><font color="Green" title="E61">A6</font></span></a>, <a class="txt" href="glib_007.html#E35"><span class="lab"><font color="Green" title="E30">Lm7</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"> ( <font color="Maroon" title="c4">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c3">v1</font> or <font color="Maroon" title="c4">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c2">v</font> )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c7">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E14:87"/><span class="lab"><font color="Green" title="E63">A8</font></span>: 
<font color="Maroon" title="c5">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:87"><span class="lab"><font color="Green" title="E59">A4</font></span></a>, <a class="ref" href="card_1.html#T29" onmouseover="rs('card_1/T29')" onmouseout="rh()">CARD_1:29</a></span>;<br/>
<a NAME="E15:87"/><span class="lab"><font color="Green" title="E64">A9</font></span>: 
<font color="Maroon" title="c5">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">e1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:87"><span class="lab"><font color="Green" title="E61">A6</font></span></a>, <a class="txt" href="#E14:87"><span class="lab"><font color="Green" title="E63">A8</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<a NAME="E16:87"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A10</font></span>: 
 <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">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">e1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:87"><span class="lab"><font color="Green" title="E59">A4</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c8">f</font>, <font color="Maroon" title="c9">g</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c5">E</font>,<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">v1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">v</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span><span class="kw"> such that </span><br/><a NAME="E18:87"/><span class="lab"><font color="Green" title="E66">A11</font></span>: 
 <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">G2</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">and </span><br/><a NAME="E19:87"/><span class="lab"><font color="Green" title="E67">A12</font></span>: 
 <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">G2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c9">g</font>
 <span class="kw">and </span><br/><a NAME="E20:87"/><span class="lab"><font color="Green" title="E68">A13</font></span>: 
 for <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">E</font> holds <br/>( <font color="Olive" title="b1">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c8">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font>,<font color="Maroon" title="c9">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font>,<font color="Maroon" title="c4">G1</font> &amp; ( <font color="Maroon" title="c8">f</font> <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> <font color="Maroon" title="c2">v</font> implies <font color="Maroon" title="c9">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> ) &amp; ( <font color="Maroon" title="c9">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> implies <font color="Maroon" title="c8">f</font> <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> <font color="Maroon" title="c2">v</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="txt" href="#E2:87"><span class="lab"><font color="Green" title="E57">A2</font></span></a>, <a class="txt" href="#E5:87"><span class="lab"><font color="Green" title="E59">A4</font></span></a>, <a class="ref" href="glib_007.html#T52" target="_self" onmouseover="rs('glib_007/T52')" onmouseout="rh()">Th52</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">f</font> = <font color="Maroon" title="c8">f</font>, <font color="Maroon" title="c11">g</font> = <font color="Maroon" title="c9">g</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">e1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c2">v</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:87"><span class="lab"><font color="Green" title="E64">A9</font></span></a>, <a class="ref" href="enumset1.html#T1" onmouseover="rs('enumset1/T1')" onmouseout="rh()">ENUMSET1:1</a></span>;<br/>
<a NAME="E22:87"/><span class="lab"><font color="Green" title="E69">A14</font></span>: 
<font color="Maroon" title="c6">e1</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c11">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c4">G1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:87"><span class="lab"><font color="Green" title="E61">A6</font></span></a>, <a class="txt" href="#E20:87"><span class="lab"><font color="Green" title="E68">A13</font></span></a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="87_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="E1:87_1"/>
( <font color="Maroon" title="c6">e1</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> or <font color="Maroon" title="c6">e1</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">G1</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:87"><span class="lab"><font color="Green" title="E61">A6</font></span></a>, <a class="ref" href="glib_000.html#T16" onmouseover="rs('glib_000/T16')" onmouseout="rh()">GLIB_000:16</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="87_1_1"><span class="kw">suppose </span></a><a NAME="E1:87_1_1"/>
<font color="Maroon" title="c6">e1</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c3">v1</font> or <font color="Maroon" title="c4">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c2">v</font> )</span><br/><div class="add"><a NAME="E2:87_1_1"/><span class="kw">then </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="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</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="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D14" onmouseover="rs('glib_000/D14')" onmouseout="rh()">GLIB_000:def 14</a></span>;<br/><a NAME="E3:87_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A15</font></span>: 
( <font color="Maroon" title="c3">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">e1</font> &amp; <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">e1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:87"><span class="lab"><font color="Green" title="E69">A14</font></span></a>, <a class="ref" href="glib_000.html#D14" onmouseover="rs('glib_000/D14')" onmouseout="rh()">GLIB_000:def 14</a></span>;<br/><a NAME="E4:87_1_1"/>
 for <font color="Olive" title="b1">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c10">f</font> holds <br/><font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87_1_1"><span class="lab"><font color="Green" title="E70">A15</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><a NAME="E5:87_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c10">f</font></span>)</span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c3">v1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T11" onmouseover="rs('funcop_1/T11')" onmouseout="rh()">FUNCOP_1:11</a></span>;<br/><a NAME="E6:87_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">e1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c3">v1</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="E7:87_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A16</font></span>: 
 <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">G2</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">e1</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c3">v1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:87"><span class="lab"><font color="Green" title="E66">A11</font></span></a>, <a class="ref" href="funcop_1.html#D9" onmouseover="rs('funcop_1/D9')" onmouseout="rh()">FUNCOP_1:def 9</a></span>;<br/><a NAME="E8:87_1_1"/>
 for <font color="Olive" title="b1">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c11">g</font> holds <br/><font color="Maroon" title="c11">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87_1_1"><span class="lab"><font color="Green" title="E70">A15</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><a NAME="E9:87_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">g</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c11">g</font></span>)</span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">v</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T11" onmouseover="rs('funcop_1/T11')" onmouseout="rh()">FUNCOP_1:11</a></span>;<br/><a NAME="E10:87_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">g</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">e1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">v</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="E11:87_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">e1</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c2">v</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#D9" onmouseover="rs('funcop_1/D9')" onmouseout="rh()">FUNCOP_1:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E12:87_1_1"/>
( <font color="Maroon" title="c4">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c3">v1</font> or <font color="Maroon" title="c4">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c2">v</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="txt" href="#E12:87"><span class="lab"><font color="Green" title="E62">A7</font></span></a>, <a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E58">A3</font></span></a>, <a class="txt" href="#E16:87"><span class="lab"><font color="Green" title="E65">A10</font></span></a>, <a class="txt" href="#E7:87_1_1"><span class="lab"><font color="Green" title="E71">A16</font></span></a>, <a class="ref" href="glib_006.html#D12" onmouseover="rs('glib_006/D12')" onmouseout="rh()">GLIB_006:def 12</a>, <a class="txt" href="#E19:87"><span class="lab"><font color="Green" title="E67">A12</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="87_1_2"><span class="kw">suppose </span></a><a NAME="E1:87_1_2"/>
<font color="Maroon" title="c6">e1</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">G1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c3">v1</font> or <font color="Maroon" title="c4">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c2">v</font> )</span><br/><div class="add"><a NAME="E2:87_1_2"/><span class="kw">then </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="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</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="c4">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D14" onmouseover="rs('glib_000/D14')" onmouseout="rh()">GLIB_000:def 14</a></span>;<br/><a NAME="E3:87_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A17</font></span>: 
( <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">e1</font> &amp; <font color="Maroon" title="c3">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">e1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:87"><span class="lab"><font color="Green" title="E69">A14</font></span></a>, <a class="ref" href="glib_000.html#D14" onmouseover="rs('glib_000/D14')" onmouseout="rh()">GLIB_000:def 14</a></span>;<br/><a NAME="E4:87_1_2"/>
 for <font color="Olive" title="b1">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c10">f</font> holds <br/><font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87_1_2"><span class="lab"><font color="Green" title="E70">A17</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><a NAME="E5:87_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c10">f</font></span>)</span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">v</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T11" onmouseover="rs('funcop_1/T11')" onmouseout="rh()">FUNCOP_1:11</a></span>;<br/><a NAME="E6:87_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">e1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">v</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="E7:87_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A18</font></span>: 
 <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">G2</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">e1</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c2">v</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:87"><span class="lab"><font color="Green" title="E66">A11</font></span></a>, <a class="ref" href="funcop_1.html#D9" onmouseover="rs('funcop_1/D9')" onmouseout="rh()">FUNCOP_1:def 9</a></span>;<br/><a NAME="E8:87_1_2"/>
 for <font color="Olive" title="b1">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c11">g</font> holds <br/><font color="Maroon" title="c11">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87_1_2"><span class="lab"><font color="Green" title="E70">A17</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><a NAME="E9:87_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">g</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c11">g</font></span>)</span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c3">v1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T11" onmouseover="rs('funcop_1/T11')" onmouseout="rh()">FUNCOP_1:11</a></span>;<br/><a NAME="E10:87_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">g</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">e1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c3">v1</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="E11:87_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">e1</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c3">v1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#D9" onmouseover="rs('funcop_1/D9')" onmouseout="rh()">FUNCOP_1:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E12:87_1_2"/>
( <font color="Maroon" title="c4">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c3">v1</font> or <font color="Maroon" title="c4">G1</font> is    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c2">v</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="txt" href="#E12:87"><span class="lab"><font color="Green" title="E62">A7</font></span></a>, <a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E58">A3</font></span></a>, <a class="txt" href="#E16:87"><span class="lab"><font color="Green" title="E65">A10</font></span></a>, <a class="txt" href="#E7:87_1_2"><span class="lab"><font color="Green" title="E71">A18</font></span></a>, <a class="ref" href="glib_006.html#D12" onmouseover="rs('glib_006/D12')" onmouseout="rh()">GLIB_006:def 12</a>, <a class="txt" href="#E19:87"><span class="lab"><font color="Green" title="E67">A12</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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