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<span class="kw">let </span><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">N</font> being   <a href="net_1.html#L1" title="NET_1:struct.1">Net</a>   st <font color="Maroon" title="c1">x</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="net_1.html#U2" title="NET_1:sel.2">Transitions</a> of <font color="Olive" title="b1">N</font> &amp; the <a href="net_1.html#U2" title="NET_1:sel.2">Transitions</a> of <font color="Olive" title="b1">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/><font color="Maroon" title="c1">x</font> is    <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="Olive" title="b1">N</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">N</font> be    <a href="net_1.html#L1" title="NET_1:struct.1">Net</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">x</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="net_1.html#U2" title="NET_1:sel.2">Transitions</a> of <font color="Maroon" title="c2">N</font> &amp; the <a href="net_1.html#U2" title="NET_1:sel.2">Transitions</a> of <font color="Maroon" title="c2">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <font color="Maroon" title="c1">x</font> is    <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> )</span><br/>



<a NAME="E1:11"/><span class="lab"><font color="Green" title="E2">A1</font></span>: 
the <a href="net_1.html#U2" title="NET_1:sel.2">Transitions</a> of <font color="Maroon" title="c2">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c2">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:11"/>
( <font color="Maroon" title="c1">x</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="net_1.html#U2" title="NET_1:sel.2">Transitions</a> of <font color="Maroon" title="c2">N</font> &amp; the <a href="net_1.html#U2" title="NET_1:sel.2">Transitions</a> of <font color="Maroon" title="c2">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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">x</font> is    <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></span><br/>

<span class="kw">hence </span><a NAME="E3:11"/>
<font color="Maroon" title="c1">x</font> is    <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E2">A1</font></span></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</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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