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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</font> implies ( ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a> ) ) )</span><br/>



<b>assume </b><a NAME="E1:181"/><i><font color="Green" title="E74">A1</font></i>: 
<font color="Maroon" title="c1">G1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a> ) )</span><br/>

<a NAME="E2:181"/><b>then </b><i><font color="Green" title="E75">A2</font></i>: 
(  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c2">G2</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c2">G2</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c2">G2</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c2">G2</font> )
 
<b>by </b><i><a class="ref" href="glib_000.html#D36" target="_self" title="GLIB_000:def.36">Def36</a></i>;<br/>
<b>thus </b><a NAME="E3:181"/>
( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> )
 <b>by </b><i><a class="txt" href="#E2:181"><i><font color="Green" title="E75">A2</font></i></a>, <a class="ref" href="glib_000.html#D19" target="_self" title="GLIB_000:def.19">Def19</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a> ) )</span><br/>

<div><i><font color="Green" title="E76">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="181_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:181_1"/>
<font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a></span><br/><a NAME="E2:181_1"/><b>then </b>
for <font color="Olive" title="b1">e</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <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="c2">G2</font> or  not <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="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> )
 <b>by </b><i><a class="txt" href="#E2:181"><i><font color="Green" title="E75">A2</font></i></a>, <a class="ref" href="glib_000.html#D20" target="_self" title="GLIB_000:def.20">Def20</a></i>;<br/><b>hence </b><a NAME="E3:181_1"/>
<font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a>
 <b>by </b><i><a class="ref" href="glib_000.html#D20" target="_self" title="GLIB_000:def.20">Def20</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:181"/>
( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a> ) )</span><br/>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a> ) )</span>
<div class="add"><b>assume </b><a NAME="E1:181_2"/>
<font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a></span><br/><a NAME="E2:181_2"/><b>then </b>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</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="c2">G2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="#E2:181"><i><font color="Green" title="E75">A2</font></i></a>, <a class="ref" href="glib_000.html#D21" target="_self" title="GLIB_000:def.21">Def21</a></i>;<br/><b>hence </b><a NAME="E3:181_2"/>
<font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a>
 <b>by </b><i><a class="ref" href="glib_000.html#D21" target="_self" title="GLIB_000:def.21">Def21</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<div><i><font color="Green" title="E77">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="181_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:181_3"/><i><font color="Green" title="E78">A5</font></i>: 
<font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="181_3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">e1</font>, <font color="Maroon" title="c4">e2</font>, <font color="Maroon" title="c5">v1</font>, <font color="Maroon" title="c6">v2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c5">v1</font>,<font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c2">G2</font> &amp; <font color="Maroon" title="c4">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c5">v1</font>,<font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c2">G2</font> implies <font color="Maroon" title="c3">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e2</font> )</span><br/><b>assume </b><a NAME="E1:181_3_1"/>
( <font color="Maroon" title="c3">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c5">v1</font>,<font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c2">G2</font> &amp; <font color="Maroon" title="c4">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c5">v1</font>,<font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c2">G2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e2</font></span><br/><a NAME="E2:181_3_1"/><b>then </b>
( <font color="Maroon" title="c3">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c5">v1</font>,<font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c1">G1</font> &amp; <font color="Maroon" title="c4">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c5">v1</font>,<font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c1">G1</font> )
 <b>by </b><i><a class="txt" href="#E1:181"><i><font color="Green" title="E74">A1</font></i></a>, <a class="ref" href="glib_000.html#T91" target="_self" title="GLIB_000:th.91">Th91</a></i>;<br/><b>hence </b><a NAME="E3:181_3_1"/>
<font color="Maroon" title="c3">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e2</font>
 <b>by </b><i><a class="txt" href="#E1:181_3"><i><font color="Green" title="E78">A5</font></i></a>, <a class="ref" href="glib_000.html#D22" target="_self" title="GLIB_000:def.22">Def22</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E3:181_3"/>
<font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a>
 <b>by </b><i><a class="ref" href="glib_000.html#D22" target="_self" title="GLIB_000:def.22">Def22</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:181"/>
( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a> ) )</span><br/>

<div><i><font color="Green" title="E78">A6</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="181_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:181_4"/><i><font color="Green" title="E79">A7</font></i>: 
<font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="181_4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">e1</font>, <font color="Maroon" title="c4">e2</font>, <font color="Maroon" title="c5">v1</font>, <font color="Maroon" title="c6">v2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">e1</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v1</font>,<font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c2">G2</font> &amp; <font color="Maroon" title="c4">e2</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v1</font>,<font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c2">G2</font> implies <font color="Maroon" title="c3">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e2</font> )</span><br/><b>assume </b><a NAME="E1:181_4_1"/>
( <font color="Maroon" title="c3">e1</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v1</font>,<font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c2">G2</font> &amp; <font color="Maroon" title="c4">e2</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v1</font>,<font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c2">G2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e2</font></span><br/><a NAME="E2:181_4_1"/><b>then </b>
( <font color="Maroon" title="c3">e1</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v1</font>,<font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c1">G1</font> &amp; <font color="Maroon" title="c4">e2</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v1</font>,<font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c1">G1</font> )
 <b>by </b><i><a class="txt" href="#E1:181"><i><font color="Green" title="E74">A1</font></i></a>, <a class="ref" href="glib_000.html#T91" target="_self" title="GLIB_000:th.91">Th91</a></i>;<br/><b>hence </b><a NAME="E3:181_4_1"/>
<font color="Maroon" title="c3">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e2</font>
 <b>by </b><i><a class="txt" href="#E1:181_4"><i><font color="Green" title="E79">A7</font></i></a>, <a class="ref" href="glib_000.html#D23" target="_self" title="GLIB_000:def.23">Def23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E3:181_4"/>
<font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a>
 <b>by </b><i><a class="ref" href="glib_000.html#D23" target="_self" title="GLIB_000:def.23">Def23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E10:181"/>
( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> ) &amp; ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a> ) )</span><br/>

<b>thus </b><a NAME="E11:181"/>
( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> )
 <b>by </b><i><a class="txt" href="#E4:181"><i><font color="Green" title="E76">A3</font></i></a>, <a class="txt" href="#E7:181"><i><font color="Green" title="E77">A4</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a> )</span><br/>

<b>thus </b><a NAME="E12:181"/>
( <font color="Maroon" title="c1">G1</font> is <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a> )
 <b>by </b><i><a class="txt" href="#E4:181"><i><font color="Green" title="E76">A3</font></i></a>, <a class="txt" href="#E9:181"><i><font color="Green" title="E78">A6</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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