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<b>let </b><font color="Maroon" title="c3">G1</font>, <font color="Maroon" title="c4">G2</font> be  <a href="graph_1.html#V1" title="GRAPH_1:attr.1">strict</a> <a href="graph_1.html#NM1" title="GRAPH_1:NM.1">Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( the <a href="graph_1.html#U3" title="GRAPH_1:sel.3">Source</a> of <font color="Maroon" title="c3">G1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="graph_1.html#U3" title="GRAPH_1:sel.3">Source</a> of <font color="Maroon" title="c4">G2</font> &amp; the <a href="graph_1.html#U4" title="GRAPH_1:sel.4">Target</a> of <font color="Maroon" title="c3">G1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="graph_1.html#U4" title="GRAPH_1:sel.4">Target</a> of <font color="Maroon" title="c4">G2</font> &amp;  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G1</font> <a href="graph_1.html#K1" title="GRAPH_1:func.1">\/</a> <font color="Maroon" title="c4">G2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c3">G1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c4">G2</font></span>)</span> &amp; not <font color="Maroon" title="c3">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c4">G2</font> implies <font color="Maroon" title="c4">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c3">G1</font> )</span><br/>

<b>assume </b><a NAME="E1:68"/><i><font color="Green" title="E39">A1</font></i>: 
( the <a href="graph_1.html#U3" title="GRAPH_1:sel.3">Source</a> of <font color="Maroon" title="c3">G1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="graph_1.html#U3" title="GRAPH_1:sel.3">Source</a> of <font color="Maroon" title="c4">G2</font> &amp; the <a href="graph_1.html#U4" title="GRAPH_1:sel.4">Target</a> of <font color="Maroon" title="c3">G1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="graph_1.html#U4" title="GRAPH_1:sel.4">Target</a> of <font color="Maroon" title="c4">G2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G1</font> <a href="graph_1.html#K1" title="GRAPH_1:func.1">\/</a> <font color="Maroon" title="c4">G2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c3">G1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c4">G2</font></span>)</span> or <font color="Maroon" title="c3">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c4">G2</font> or <font color="Maroon" title="c4">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c3">G1</font> )</span><br/>

<b>assume </b><a NAME="E2:68"/><i><font color="Green" title="E40">A2</font></i>: 
 <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G1</font> <a href="graph_1.html#K1" title="GRAPH_1:func.1">\/</a> <font color="Maroon" title="c4">G2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c3">G1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c4">G2</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c4">G2</font> or <font color="Maroon" title="c4">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c3">G1</font> )</span><br/>

<a NAME="E3:68"/><i><font color="Green" title="E41">A3</font></i>: 
<font color="Maroon" title="c3">G1</font> <a href="graph_1.html#K1" title="GRAPH_1:func.1">\/</a> <font color="Maroon" title="c4">G2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G1</font> <a href="graph_1.html#K1" title="GRAPH_1:func.1">\/</a> <font color="Maroon" title="c4">G2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="graph_1.html#T31" target="_self" title="GRAPH_1:th.31">Th31</a></i>;<br/>
<div><i><font color="Green" title="E42">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="68_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:68_1"/>
<font color="Maroon" title="c3">G1</font> <a href="graph_1.html#K1" title="GRAPH_1:func.1">\/</a> <font color="Maroon" title="c4">G2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c3">G1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c3">G1</font></span><br/><a NAME="E2:68_1"/><b>then </b>
<font color="Maroon" title="c3">G1</font> <a href="graph_1.html#K1" title="GRAPH_1:func.1">\/</a> <font color="Maroon" title="c4">G2</font> is    <a href="graph_1.html#M3" title="GRAPH_1:mode.3">Subgraph</a> of <font color="Maroon" title="c3">G1</font>
 <b>by </b><i><a class="ref" href="graph_1.html#D24" target="_self" title="GRAPH_1:def.24">Def24</a></i>;<br/><a NAME="E3:68_1"/><b>then </b><i><font color="Green" title="E43">A5</font></i>: 
<font color="Maroon" title="c3">G1</font> <a href="graph_1.html#K1" title="GRAPH_1:func.1">\/</a> <font color="Maroon" title="c4">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c3">G1</font>
 <b>by </b><i><a class="ref" href="graph_1.html#D23" target="_self" title="GRAPH_1:def.23">Def23</a></i>;<br/><a NAME="E4:68_1"/>
<font color="Maroon" title="c3">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c3">G1</font> <a href="graph_1.html#K1" title="GRAPH_1:func.1">\/</a> <font color="Maroon" title="c4">G2</font>
 <b>by </b><i><a class="txt" href="graph_1.html#E1:68"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="graph_1.html#T19" target="_self" title="GRAPH_1:th.19">Th19</a></i>;<br/><a NAME="E5:68_1"/><b>then </b>
<font color="Maroon" title="c3">G1</font> <a href="graph_1.html#K1" title="GRAPH_1:func.1">\/</a> <font color="Maroon" title="c4">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">G1</font>
 <b>by </b><i><a class="txt" href="graph_1.html#E3:68_1"><i><font color="Green" title="E43">A5</font></i></a>, <a class="ref" href="graph_1.html#T16" target="_self" title="GRAPH_1:th.16">Th16</a></i>;<br/><b>hence </b><a NAME="E6:68_1"/>
<font color="Maroon" title="c4">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c3">G1</font>
 <b>by </b><i><a class="txt" href="graph_1.html#E1:68"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="graph_1.html#T24" target="_self" title="GRAPH_1:th.24">Th24</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><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:68_2"/>
<font color="Maroon" title="c3">G1</font> <a href="graph_1.html#K1" title="GRAPH_1:func.1">\/</a> <font color="Maroon" title="c4">G2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c4">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">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c4">G2</font></span><br/><a NAME="E2:68_2"/><b>then </b>
<font color="Maroon" title="c3">G1</font> <a href="graph_1.html#K1" title="GRAPH_1:func.1">\/</a> <font color="Maroon" title="c4">G2</font> is    <a href="graph_1.html#M3" title="GRAPH_1:mode.3">Subgraph</a> of <font color="Maroon" title="c4">G2</font>
 <b>by </b><i><a class="ref" href="graph_1.html#D24" target="_self" title="GRAPH_1:def.24">Def24</a></i>;<br/><a NAME="E3:68_2"/><b>then </b><i><font color="Green" title="E43">A6</font></i>: 
<font color="Maroon" title="c3">G1</font> <a href="graph_1.html#K1" title="GRAPH_1:func.1">\/</a> <font color="Maroon" title="c4">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c4">G2</font>
 <b>by </b><i><a class="ref" href="graph_1.html#D23" target="_self" title="GRAPH_1:def.23">Def23</a></i>;<br/><a NAME="E4:68_2"/>
<font color="Maroon" title="c4">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c3">G1</font> <a href="graph_1.html#K1" title="GRAPH_1:func.1">\/</a> <font color="Maroon" title="c4">G2</font>
 <b>by </b><i><a class="txt" href="graph_1.html#E1:68"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="graph_1.html#T19" target="_self" title="GRAPH_1:th.19">Th19</a></i>;<br/><a NAME="E5:68_2"/><b>then </b>
<font color="Maroon" title="c3">G1</font> <a href="graph_1.html#K1" title="GRAPH_1:func.1">\/</a> <font color="Maroon" title="c4">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G2</font>
 <b>by </b><i><a class="txt" href="graph_1.html#E3:68_2"><i><font color="Green" title="E43">A6</font></i></a>, <a class="ref" href="graph_1.html#T16" target="_self" title="GRAPH_1:th.16">Th16</a></i>;<br/><b>hence </b><a NAME="E6:68_2"/>
<font color="Maroon" title="c3">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c4">G2</font>
 <b>by </b><i><a class="txt" href="graph_1.html#E1:68"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="graph_1.html#T24" target="_self" title="GRAPH_1:th.24">Th24</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="E6:68"/>
( <font color="Maroon" title="c3">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c4">G2</font> or <font color="Maroon" title="c4">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c3">G1</font> )
 <b>by </b><i><a class="txt" href="graph_1.html#E2:68"><i><font color="Green" title="E40">A2</font></i></a>, <a class="txt" href="graph_1.html#E3:68"><i><font color="Green" title="E41">A3</font></i></a>, <a class="txt" href="graph_1.html#E4:68"><i><font color="Green" title="E42">A4</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</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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