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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>





<b>assume </b><a NAME="E1:43"/>
<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="c2">G1</font>,<font color="Maroon" title="c3">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">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"/><b>then </b>
( 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; 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> &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> )
 
<b>by </b><i><a class="ref" href="graph_1.html#D4" target="_self" title="GRAPH_1:def.4">Def3</a></i>;<br/>
<a NAME="E3:43"/><b>then </b>
( 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> &amp; the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</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#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">G1</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="c3">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G1</font> )
 
<b>by </b><i><a class="ref" href="graph_1.html#T8" target="_self" title="GRAPH_1:th.8">Th8</a></i>;<br/>
<b>hence </b><a NAME="E4:43"/>
<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>
 <b>by </b><i><a class="ref" href="graph_1.html#D4" target="_self" title="GRAPH_1:def.4">Def3</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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