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<div><span class="kw">theorem </span><a NAME="T9"><span class="comment"><font color="firebrick">:: PETRI_3:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">CPN</font> being   <a href="petri_3.html#V4" title="PETRI_3:attr.4">with-nontrivial-ColoredSet</a>  <a href="petri_2.html#NM3" title="PETRI_2:NM.3">Colored-PT-net</a><br/>  for <font color="Olive" title="b2">m</font> being   <a href="petri_3.html#NM6" title="PETRI_3:NM.6">colored-state</a> of <font color="Olive" title="b1">CPN</font><br/>  for <font color="Olive" title="b3">t</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive" title="b1">CPN</font><br/>  for <font color="Olive" title="b4">D0</font> being    <a href="petri_2.html#M1" title="PETRI_2:mode.1">thin_cylinder</a> of  the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Olive" title="b1">CPN</font>, <a href="petri.html#K8" title="PETRI:func.8">*'</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b3">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span><br/>  for <font color="Olive" title="b5">D1</font> being    <a href="petri_2.html#M1" title="PETRI_2:mode.1">thin_cylinder</a> of  the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Olive" title="b1">CPN</font>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b3">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="petri.html#K9" title="PETRI:func.9">*'</a> <br/>  for <font color="Olive" title="b6">ColD0</font> being   <a href="petri_3.html#NM4" title="PETRI_3:NM.4">color-threshold</a> of <font color="Olive" title="b4">D0</font><br/>  for <font color="Olive" title="b7">ColD1</font> being   <a href="petri_3.html#NM4" title="PETRI_3:NM.4">color-threshold</a> of <font color="Olive" title="b5">D1</font><br/>  for <font color="Olive" title="b8">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Olive" title="b1">CPN</font><br/>  for <font color="Olive" title="b9">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">CPN</font>  st <font color="Olive" title="b3">t</font> is  <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a>  holds <br/>( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">m</font> <a href="petri_3.html#K5" title="PETRI_3:func.5">.</a> <font color="Olive" title="b9">p</font></span>)</span> <a href="petri_3.html#K6" title="PETRI_3:func.6">.</a> <font color="Olive" title="b8">x</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="petri_3.html#K10" title="PETRI_3:func.10">firing_result</a> (<font color="Olive" title="b6">ColD0</font>,<font color="Olive" title="b7">ColD1</font>,<font color="Olive" title="b2">m</font>,<font color="Olive" title="b9">p</font>)</span>)</span> <a href="petri_3.html#K6" title="PETRI_3:func.6">.</a> <font color="Olive" title="b8">x</font> &amp; <span class="p1">(<span class="default"><a href="petri_3.html#K10" title="PETRI_3:func.10">firing_result</a> (<font color="Olive" title="b6">ColD0</font>,<font color="Olive" title="b7">ColD1</font>,<font color="Olive" title="b2">m</font>,<font color="Olive" title="b9">p</font>)</span>)</span> <a href="petri_3.html#K6" title="PETRI_3:func.6">.</a> <font color="Olive" title="b8">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">m</font> <a href="petri_3.html#K5" title="PETRI_3:func.5">.</a> <font color="Olive" title="b9">p</font></span>)</span> <a href="petri_3.html#K6" title="PETRI_3:func.6">.</a> <font color="Olive" title="b8">x</font> )</div></div>
