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<span class="kw">let </span><font color="Maroon" title="c1">PTN</font> be   <a href="petri.html#NM2" title="PETRI:NM.2">Petri_net</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PTN</font> holds   <a href="petri.html#K6" title="PETRI:func.6">*'</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">S</font> <a href="petri.html#K12" title="PETRI:func.12">.:</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">S</font> <a href="petri.html#K7" title="PETRI:func.7">*'</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PTN</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="petri.html#K6" title="PETRI:func.6">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K12" title="PETRI:func.12">.:</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">S</font> <a href="petri.html#K7" title="PETRI:func.7">*'</a> </span><br/>



<span class="kw">thus </span><a NAME="E1:45"/>
 <a href="petri.html#K6" title="PETRI:func.6">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K12" title="PETRI:func.12">.:</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">S</font> <a href="petri.html#K7" title="PETRI:func.7">*'</a> 
  <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="xboole_0.html#D10" onmouseover="rs('xboole_0/D10')" onmouseout="rh()">XBOOLE_0:def 10</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">S</font> <a href="petri.html#K7" title="PETRI:func.7">*'</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="petri.html#K6" title="PETRI:func.6">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K12" title="PETRI:func.12">.:</a></span>)</span></span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="45_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri.html#K6" title="PETRI:func.6">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K12" title="PETRI:func.12">.:</a></span>)</span> or <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="petri.html#K7" title="PETRI:func.7">*'</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:45_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri.html#K6" title="PETRI:func.6">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K12" title="PETRI:func.12">.:</a></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="petri.html#K7" title="PETRI:func.7">*'</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">f</font> being   <a href="petri.html#NM8" title="PETRI:NM.8">T-S_arc</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">PTN</font> <a href="petri.html#K11" title="PETRI:func.11">.:</a></span>)</span>, <font color="Maroon" title="c5">s</font> being   <a href="petri.html#NM3" title="PETRI:NM.3">place</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">PTN</font> <a href="petri.html#K11" title="PETRI:func.11">.:</a></span>)</span><span class="kw"> such that </span><br/><a NAME="E3:45_1"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
<font color="Maroon" title="c5">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="petri.html#K12" title="PETRI:func.12">.:</a> 
 <span class="kw">and </span><br/><a NAME="E4:45_1"/><span class="lab"><font color="Green" title="E10">A2</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c5">s</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="petri.html#T2" target="_self" onmouseover="rs('petri/T2')" onmouseout="rh()">Th2</a></span>;<br/>
<a NAME="E5:45_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="petri.html#K15" title="PETRI:func.15">.:</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c3">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is   <a href="petri.html#NM7" title="PETRI:NM.7">S-T_arc</a> of <font color="Maroon" title="c1">PTN</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:45_1"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="relat_1.html#D7" onmouseover="rs('relat_1/D7')" onmouseout="rh()">RELAT_1:def 7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:45_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="petri.html#K7" title="PETRI:func.7">*'</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:45_1"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="petri.html#T4" target="_self" onmouseover="rs('petri/T4')" onmouseout="rh()">Th4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="petri.html#K7" title="PETRI:func.7">*'</a>  or <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri.html#K6" title="PETRI:func.6">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K12" title="PETRI:func.12">.:</a></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E2:45"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="petri.html#K7" title="PETRI:func.7">*'</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri.html#K6" title="PETRI:func.6">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K12" title="PETRI:func.12">.:</a></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">f</font> being   <a href="petri.html#NM7" title="PETRI:NM.7">S-T_arc</a> of <font color="Maroon" title="c1">PTN</font>, <font color="Maroon" title="c5">s</font> being   <a href="petri.html#NM3" title="PETRI:NM.3">place</a> of <font color="Maroon" title="c1">PTN</font><span class="kw"> such that </span><br/><a NAME="E4:45"/><span class="lab"><font color="Green" title="E9">A3</font></span>: 
<font color="Maroon" title="c5">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">S</font>
 <span class="kw">and </span><br/><a NAME="E5:45"/><span class="lab"><font color="Green" title="E10">A4</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c3">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="petri.html#T4" target="_self" onmouseover="rs('petri/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<a NAME="E6:45"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="petri.html#K13" title="PETRI:func.13">.:</a></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is   <a href="petri.html#NM8" title="PETRI:NM.8">T-S_arc</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">PTN</font> <a href="petri.html#K11" title="PETRI:func.11">.:</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:45"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="ref" href="relat_1.html#D7" onmouseover="rs('relat_1/D7')" onmouseout="rh()">RELAT_1:def 7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:45"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri.html#K6" title="PETRI:func.6">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="petri.html#K12" title="PETRI:func.12">.:</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:45"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="ref" href="petri.html#T2" target="_self" onmouseover="rs('petri/T2')" onmouseout="rh()">Th2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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