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<span class="kw">let </span><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font>, <font color="Maroon" title="c3">G3</font> be   <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="Red">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">G</font> being  <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">Graph</a> st <br/>( <font color="Maroon" title="c1">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Olive" title="b1">G</font> &amp; <font color="Maroon" title="c2">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Olive" title="b1">G</font> &amp; <font color="Maroon" title="c3">G3</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Olive" title="b1">G</font> ) implies <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="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> )</span><br/>





<span class="kw">given </span><font color="Maroon" title="c4">G</font> being   <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">Graph</a><span class="kw"> such that </span><a NAME="E2:46"/><span class="lab"><font color="Green" title="E22">A1</font></span>: 
<font color="Maroon" title="c1">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c4">G</font>
 <span class="kw">and </span><br/><a NAME="E3:46"/><span class="lab"><font color="Green" title="E23">A2</font></span>: 
<font color="Maroon" title="c2">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c4">G</font>
 <span class="kw">and </span><br/><a NAME="E4:46"/><span class="lab"><font color="Green" title="E24">A3</font></span>: 
<font color="Maroon" title="c3">G3</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c4">G</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <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="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span><br/>

<a NAME="E5:46"/><span class="lab"><font color="Green" title="E25">A4</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="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c4">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="ref" href="graph_1.html#T5" target="_self" title="GRAPH_1:th.5">Th5</a></span>;<br/>
<a NAME="E6:46"/><span class="lab"><font color="Green" title="E26">A5</font></span>: 
the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">G2</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c4">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:46"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="ref" href="graph_1.html#T5" target="_self" title="GRAPH_1:th.5">Th5</a></span>;<br/>
<a NAME="E7:46"/><span class="lab"><font color="Green" title="E27">A6</font></span>: 
the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c4">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:46"><span class="lab"><font color="Green" title="E24">A3</font></span></a>, <a class="ref" href="graph_1.html#T5" target="_self" title="GRAPH_1:th.5">Th5</a></span>;<br/>
<a NAME="E8:46"/><span class="lab"><font color="Green" title="E28">A7</font></span>: 
the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c4">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="ref" href="graph_1.html#T5" target="_self" title="GRAPH_1:th.5">Th5</a></span>;<br/>
<a NAME="E9:46"/><span class="lab"><font color="Green" title="E29">A8</font></span>: 
the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">G2</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c4">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:46"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="ref" href="graph_1.html#T5" target="_self" title="GRAPH_1:th.5">Th5</a></span>;<br/>
<a NAME="E10:46"/><span class="lab"><font color="Green" title="E30">A9</font></span>: 
the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c4">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:46"><span class="lab"><font color="Green" title="E24">A3</font></span></a>, <a class="ref" href="graph_1.html#T5" target="_self" title="GRAPH_1:th.5">Th5</a></span>;<br/>
<a NAME="E11:46"/><span class="lab"><font color="Green" title="E31">A10</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:46"><span class="lab"><font color="Green" title="E25">A4</font></span></a>, <a class="txt" href="#E6:46"><span class="lab"><font color="Green" title="E26">A5</font></span></a>, <a class="ref" href="partfun1.html#T139" title="PARTFUN1:th.139">PARTFUN1:139</a></span>;<br/>
<a NAME="E12:46"/><span class="lab"><font color="Green" title="E32">A11</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="c3">G3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:46"><span class="lab"><font color="Green" title="E25">A4</font></span></a>, <a class="txt" href="#E7:46"><span class="lab"><font color="Green" title="E27">A6</font></span></a>, <a class="ref" href="partfun1.html#T139" title="PARTFUN1:th.139">PARTFUN1:139</a></span>;<br/>
<a NAME="E13:46"/><span class="lab"><font color="Green" title="E33">A12</font></span>: 
the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">G2</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="c3">G3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:46"><span class="lab"><font color="Green" title="E26">A5</font></span></a>, <a class="txt" href="#E7:46"><span class="lab"><font color="Green" title="E27">A6</font></span></a>, <a class="ref" href="partfun1.html#T139" title="PARTFUN1:th.139">PARTFUN1:139</a></span>;<br/>
<a NAME="E14:46"/><span class="lab"><font color="Green" title="E34">A13</font></span>: 
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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:46"><span class="lab"><font color="Green" title="E28">A7</font></span></a>, <a class="txt" href="#E9:46"><span class="lab"><font color="Green" title="E29">A8</font></span></a>, <a class="ref" href="partfun1.html#T139" title="PARTFUN1:th.139">PARTFUN1:139</a></span>;<br/>
<a NAME="E15:46"/><span class="lab"><font color="Green" title="E35">A14</font></span>: 
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="c3">G3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:46"><span class="lab"><font color="Green" title="E28">A7</font></span></a>, <a class="txt" href="#E10:46"><span class="lab"><font color="Green" title="E30">A9</font></span></a>, <a class="ref" href="partfun1.html#T139" title="PARTFUN1:th.139">PARTFUN1:139</a></span>;<br/>
<a NAME="E16:46"/><span class="lab"><font color="Green" title="E36">A15</font></span>: 
the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">G2</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="c3">G3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:46"><span class="lab"><font color="Green" title="E29">A8</font></span></a>, <a class="txt" href="#E10:46"><span class="lab"><font color="Green" title="E30">A9</font></span></a>, <a class="ref" href="partfun1.html#T139" title="PARTFUN1:th.139">PARTFUN1:139</a></span>;<br/>
<span class="kw">thus </span><a NAME="E17:46"/>
<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="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:46"><span class="lab"><font color="Green" title="E31">A10</font></span></a>, <a class="txt" href="#E12:46"><span class="lab"><font color="Green" title="E32">A11</font></span></a>, <a class="txt" href="#E13:46"><span class="lab"><font color="Green" title="E33">A12</font></span></a>, <a class="txt" href="#E14:46"><span class="lab"><font color="Green" title="E34">A13</font></span></a>, <a class="txt" href="#E15:46"><span class="lab"><font color="Green" title="E35">A14</font></span></a>, <a class="txt" href="#E16:46"><span class="lab"><font color="Green" title="E36">A15</font></span></a>, <a class="ref" href="graph_1.html#T9" target="_self" title="GRAPH_1:th.9">Th9</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/>


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