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<span class="kw">let </span><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font> be   <a href="graph_1.html#V1" title="GRAPH_1:attr.1">strict</a>  <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">G2</font> &amp;  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">G2</font> &amp;  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">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#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c1">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#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c2">G2</font></span>)</span> &amp;  not <font color="Maroon" title="c1">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c2">G2</font> implies <font color="Maroon" title="c2">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c1">G1</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:63"/><span class="lab"><font color="Green" title="E31">A1</font></span>: 
(  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">G2</font> &amp;  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">G2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">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#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c1">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#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c2">G2</font></span>)</span> or <font color="Maroon" title="c1">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c2">G2</font> or <font color="Maroon" title="c2">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c1">G1</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:63"/><span class="lab"><font color="Green" title="E32">A2</font></span>: 
 <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">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#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c1">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#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c2">G2</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c2">G2</font> or <font color="Maroon" title="c2">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c1">G1</font> )</span><br/>

<a NAME="E3:63"/><span class="lab"><font color="Green" title="E33">A3</font></span>: 
<font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="graph_1.html#T29" target="_self" title="GRAPH_1:th.29">Th31</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E34">A4</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:63_1"/>
<font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c1">G1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c1">G1</font></span><br/><a NAME="E2:63_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font> is    <a href="graph_1.html#M3" title="GRAPH_1:mode.3">Subgraph</a> of <font color="Maroon" title="c1">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="graph_1.html#D23" target="_self" title="GRAPH_1:def.23">Def25</a></span>;<br/><a NAME="E3:63_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A5</font></span>: 
<font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c1">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="graph_1.html#D22" target="_self" title="GRAPH_1:def.22">Def24</a></span>;<br/><a NAME="E4:63_1"/>
<font color="Maroon" title="c1">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="graph_1.html#T19" target="_self" title="GRAPH_1:th.19">Th19</a></span>;<br/><a NAME="E5:63_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:63_1"><span class="lab"><font color="Green" title="E35">A5</font></span></a>, <a class="ref" href="graph_1.html#T16" target="_self" title="GRAPH_1:th.16">Th16</a></span>;<br/><span class="kw">hence </span><a NAME="E6:63_1"/>
<font color="Maroon" title="c2">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c1">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="graph_1.html#T24" target="_self" title="GRAPH_1:th.24">Th24</a></span>; <a class="txt" 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="hs2(this)" href="javascript:()" title="63_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:63_2"/>
<font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c2">G2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c2">G2</font></span><br/><a NAME="E2:63_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font> is    <a href="graph_1.html#M3" title="GRAPH_1:mode.3">Subgraph</a> of <font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="graph_1.html#D23" target="_self" title="GRAPH_1:def.23">Def25</a></span>;<br/><a NAME="E3:63_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A6</font></span>: 
<font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="graph_1.html#D22" target="_self" title="GRAPH_1:def.22">Def24</a></span>;<br/><a NAME="E4:63_2"/>
<font color="Maroon" title="c2">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="graph_1.html#T19" target="_self" title="GRAPH_1:th.19">Th19</a></span>;<br/><a NAME="E5:63_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:63_2"><span class="lab"><font color="Green" title="E35">A6</font></span></a>, <a class="ref" href="graph_1.html#T16" target="_self" title="GRAPH_1:th.16">Th16</a></span>;<br/><span class="kw">hence </span><a NAME="E6:63_2"/>
<font color="Maroon" title="c1">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="graph_1.html#T24" target="_self" title="GRAPH_1:th.24">Th24</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E6:63"/>
( <font color="Maroon" title="c1">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c2">G2</font> or <font color="Maroon" title="c2">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c1">G1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="txt" href="#E3:63"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="txt" href="#E4:63"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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