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<b>let </b><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">N</font> be   <a href="net_1.html#NM1" title="NET_1:NM.1">Pnet</a>;<br/><b>let </b><font color="Maroon" title="c3">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c2">N</font>;<br/>





<b>assume </b><a NAME="E1:21"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="net_1.html#U2" title="NET_1:sel.2">Transitions</a> of <font color="Maroon" title="c2">N</font>
 ;<br/>

<a NAME="E2:21"/><i><font color="Green" title="E16">A2</font></i>: 
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="net_1.html#K3" title="NET_1:func.3">Post</a> <font color="Maroon" title="c2">N</font>,<font color="Maroon" title="c3">y</font> implies  <a href="net_1.html#R2" title="NET_1:pred.2">post</a> <font color="Maroon" title="c2">N</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">x</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:21_1"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="net_1.html#K3" title="NET_1:func.3">Post</a> <font color="Maroon" title="c2">N</font>,<font color="Maroon" title="c3">y</font>
 ;<br/>

<a NAME="E2:21_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="net_1.html#U3" title="NET_1:sel.3">Flow</a> of <font color="Maroon" title="c2">N</font>
 
<b>by </b><i><a class="ref" href="net_1.html#D8" target="_self" title="NET_1:def.8">Def8</a></i>;<br/>
<b>hence </b><a NAME="E3:21_1"/>
 <a href="net_1.html#R2" title="NET_1:pred.2">post</a> <font color="Maroon" title="c2">N</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">x</font>
 <b>by </b><i><a class="txt" href="net_1.html#E1:21"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="net_1.html#D6" target="_self" title="NET_1:def.6">Def6</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:21"/>
(  <a href="net_1.html#R2" title="NET_1:pred.2">post</a> <font color="Maroon" title="c2">N</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">x</font> implies <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="net_1.html#K3" title="NET_1:func.3">Post</a> <font color="Maroon" title="c2">N</font>,<font color="Maroon" title="c3">y</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:21_2"/>
 <a href="net_1.html#R2" title="NET_1:pred.2">post</a> <font color="Maroon" title="c2">N</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">x</font>
 ;<br/>

<a NAME="E2:21_2"/><b>then </b><i><font color="Green" title="E17">A3</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="net_1.html#U3" title="NET_1:sel.3">Flow</a> of <font color="Maroon" title="c2">N</font>
 
<b>by </b><i><a class="ref" href="net_1.html#D6" target="_self" title="NET_1:def.6">Def6</a></i>;<br/>
<a NAME="E3:21_2"/><b>then </b>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="net_1.html#U1" title="NET_1:sel.1">Places</a> of <font color="Maroon" title="c2">N</font>
 
<b>by </b><i><a class="txt" href="net_1.html#E1:21"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="net_1.html#T12" target="_self" title="NET_1:th.12">Th12</a></i>;<br/>
<a NAME="E4:21_2"/><b>then </b>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c2">N</font>
 
<b>by </b><i><a class="txt" href="net_1.html#E5"><i><font color="Green" title="E4">Lm3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:21_2"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="net_1.html#K3" title="NET_1:func.3">Post</a> <font color="Maroon" title="c2">N</font>,<font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="txt" href="net_1.html#E2:21_2"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="net_1.html#D8" target="_self" title="NET_1:def.8">Def8</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:21"/>
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="net_1.html#K3" title="NET_1:func.3">Post</a> <font color="Maroon" title="c2">N</font>,<font color="Maroon" title="c3">y</font> iff  <a href="net_1.html#R2" title="NET_1:pred.2">post</a> <font color="Maroon" title="c2">N</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">x</font> )
 <b>by </b><i><a class="txt" href="net_1.html#E2:21"><i><font color="Green" title="E16">A2</font></i></a></i>;<br/>


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