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<span class="kw">let </span><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">G1</font>, <font color="Maroon" title="c3">G2</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"> ( <font color="Maroon" title="c1">G</font> <a href="graph_1.html#R1" title="GRAPH_1:pred.1">is_sum_of</a> <font color="Maroon" title="c2">G1</font>,<font color="Maroon" title="c3">G2</font> implies <font color="Maroon" title="c1">G</font> <a href="graph_1.html#R1" title="GRAPH_1:pred.1">is_sum_of</a> <font color="Maroon" title="c3">G2</font>,<font color="Maroon" title="c2">G1</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:43"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
<font color="Maroon" title="c1">G</font> <a href="graph_1.html#R1" title="GRAPH_1:pred.1">is_sum_of</a> <font color="Maroon" title="c2">G1</font>,<font color="Maroon" title="c3">G2</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="c1">G</font> <a href="graph_1.html#R1" title="GRAPH_1:pred.1">is_sum_of</a> <font color="Maroon" title="c3">G2</font>,<font color="Maroon" title="c2">G1</font></span><br/>

<a NAME="E2:43"/><span class="lab"><font color="Green" title="E22">A2</font></span>: 
the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">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">G2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="graph_1.html#D4" target="_self" title="GRAPH_1:def.4">Def4</a></span>;<br/>
<a NAME="E3:43"/><span class="lab"><font color="Green" title="E23">A3</font></span>: 
( the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">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">G2</font> &amp;  <a href="graph_1.html#G1" title="GRAPH_1:aggr.1">MultiGraphStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="graph_1.html#D4" target="_self" title="GRAPH_1:def.4">Def4</a></span>;<br/>
<a NAME="E4:43"/><span class="lab"><font color="Green" title="E24">A4</font></span>: 
the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">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="c2">G1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="graph_1.html#D4" target="_self" title="GRAPH_1:def.4">Def4</a></span>;<br/>
<a NAME="E5:43"/><span class="lab"><font color="Green" title="E25">A5</font></span>: 
 <a href="graph_1.html#G1" title="GRAPH_1:aggr.1">MultiGraphStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="txt" href="#E3:43"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="ref" href="graph_1.html#T8" target="_self" title="GRAPH_1:th.8">Th8</a></span>;<br/>
<span class="kw">thus </span><a NAME="E6:43"/>
<font color="Maroon" title="c1">G</font> <a href="graph_1.html#R1" title="GRAPH_1:pred.1">is_sum_of</a> <font color="Maroon" title="c3">G2</font>,<font color="Maroon" title="c2">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="txt" href="#E4:43"><span class="lab"><font color="Green" title="E24">A4</font></span></a>, <a class="txt" href="#E5:43"><span class="lab"><font color="Green" title="E25">A5</font></span></a>, <a class="ref" href="graph_1.html#D4" target="_self" title="GRAPH_1:def.4">Def4</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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