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<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">e</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">v1</font>, <font color="Olive" title="b3">v2</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">v2</font>,<font color="Maroon" title="c1">G</font> holds <br/>( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">v1</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a>  &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">v2</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">v1</font>, <font color="Olive" title="b2">v2</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>  st <font color="Maroon" title="c2">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c1">G</font> holds <br/>( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">v1</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a>  &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">v2</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">v1</font>, <font color="Maroon" title="c4">v2</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">e</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="c4">v2</font>,<font color="Maroon" title="c1">G</font> implies ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a>  &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a>  ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:164"/><span class="lab"><font color="Green" title="E63">A1</font></span>: 
<font color="Maroon" title="c2">e</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="c4">v2</font>,<font color="Maroon" title="c1">G</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a>  &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a>  )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="164_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="164_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:164_1_1"/>
( ( <font color="Maroon" title="c2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K26" title="GLIB_000:func.26">.edgesIn()</a>  &amp; <font color="Maroon" title="c2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesOut()</a>  ) or ( <font color="Maroon" title="c2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K26" title="GLIB_000:func.26">.edgesIn()</a>  &amp; <font color="Maroon" title="c2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesOut()</a>  ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:164"><span class="lab"><font color="Green" title="E63">A1</font></span></a>, <a class="ref" href="glib_000.html#T66" target="_self" title="GLIB_000:th.66">Th66</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="164_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:164_1_1_1"/><span class="lab"><font color="Green" title="E64">A2</font></span>: 
( <font color="Maroon" title="c2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K26" title="GLIB_000:func.26">.edgesIn()</a>  &amp; <font color="Maroon" title="c2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesOut()</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a>  &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a>  )</span><br/><div class="add"><a NAME="E2:164_1_1_1"/><span class="kw">then </span>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</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="c2">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/><font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K26" title="GLIB_000:func.26">.edgesIn()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E3:164_1_1_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K26" title="GLIB_000:func.26">.edgesIn()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/><a NAME="E4:164_1_1_1"/><span class="kw">then </span>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K26" title="GLIB_000:func.26">.edgesIn()</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T44" title="NAT_1:th.44">NAT_1:44</a></span>;<br/><a NAME="E5:164_1_1_1"/><span class="kw">then </span>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K32" title="GLIB_000:func.32">.inDegree()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T50" title="CARD_1:th.50">CARD_1:50</a></span>;<br/><span class="kw">hence </span><a NAME="E6:164_1_1_1"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a> </span><br/><a NAME="E7:164_1_1_1"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</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="c2">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/><font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesOut()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:164_1_1_1"><span class="lab"><font color="Green" title="E64">A2</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E8:164_1_1_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesOut()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/><a NAME="E9:164_1_1_1"/><span class="kw">then </span>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesOut()</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T44" title="NAT_1:th.44">NAT_1:44</a></span>;<br/><a NAME="E10:164_1_1_1"/><span class="kw">then </span>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K33" title="GLIB_000:func.33">.outDegree()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T50" title="CARD_1:th.50">CARD_1:50</a></span>;<br/><span class="kw">hence </span><a NAME="E11:164_1_1_1"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="164_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:164_1_1_2"/><span class="lab"><font color="Green" title="E64">A3</font></span>: 
( <font color="Maroon" title="c2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K26" title="GLIB_000:func.26">.edgesIn()</a>  &amp; <font color="Maroon" title="c2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesOut()</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a>  &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a>  )</span><br/><div class="add"><a NAME="E2:164_1_1_2"/><span class="kw">then </span>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</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="c2">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/><font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesOut()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E3:164_1_1_2"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesOut()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/><a NAME="E4:164_1_1_2"/><span class="kw">then </span>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesOut()</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T44" title="NAT_1:th.44">NAT_1:44</a></span>;<br/><a NAME="E5:164_1_1_2"/><span class="kw">then </span>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K33" title="GLIB_000:func.33">.outDegree()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T50" title="CARD_1:th.50">CARD_1:50</a></span>;<br/><span class="kw">hence </span><a NAME="E6:164_1_1_2"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a> </span><br/><a NAME="E7:164_1_1_2"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</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="c2">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/><font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K26" title="GLIB_000:func.26">.edgesIn()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:164_1_1_2"><span class="lab"><font color="Green" title="E64">A3</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E8:164_1_1_2"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K26" title="GLIB_000:func.26">.edgesIn()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/><a NAME="E9:164_1_1_2"/><span class="kw">then </span>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K26" title="GLIB_000:func.26">.edgesIn()</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T44" title="NAT_1:th.44">NAT_1:44</a></span>;<br/><a NAME="E10:164_1_1_2"/><span class="kw">then </span>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K32" title="GLIB_000:func.32">.inDegree()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T50" title="CARD_1:th.50">CARD_1:50</a></span>;<br/><span class="kw">hence </span><a NAME="E11:164_1_1_2"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:164"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a>  &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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