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<span class="kw">let </span><font color="Maroon" title="c1">Dftn</font> be   <a href="petri_df.html#V3" title="PETRI_DF:attr.3">With_directed_path</a>  <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">dct</font> being   <a href="petri_df.html#V2" title="PETRI_DF:attr.2">directed_path_like</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="petri_df.html#NK2" title="PETRI_DF:NK.2">places_and_trans_of</a> <font color="Maroon" title="c1">Dftn</font> holds  <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">dct</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">dct</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2</span>)</span></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="petri.html#U1" title="PETRI:sel.1">S-T_Arcs</a> of <font color="Maroon" title="c1">Dftn</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">dct</font> be   <a href="petri_df.html#V2" title="PETRI_DF:attr.2">directed_path_like</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="petri_df.html#NK2" title="PETRI_DF:NK.2">places_and_trans_of</a> <font color="Maroon" title="c1">Dftn</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"> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">dct</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">dct</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2</span>)</span></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="petri.html#U1" title="PETRI:sel.1">S-T_Arcs</a> of <font color="Maroon" title="c1">Dftn</font></span><br/>



<a NAME="E1:24"/><span class="lab"><font color="Green" title="E11">A3</font></span>: 
1 <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#T14" onmouseover="rs('nat_d/T14')" onmouseout="rh()">NAT_D:14</a></span>;<br/>
<a NAME="E2:24"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">dct</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="petri_df.html#D8" target="_self" onmouseover="rs('petri_df/D8')" onmouseout="rh()">Def5</a></span>;<br/>
<a NAME="E3:24"/><span class="kw">then </span>
1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">dct</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:24"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">dct</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">dct</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2</span>)</span></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="petri.html#U1" title="PETRI:sel.1">S-T_Arcs</a> of <font color="Maroon" title="c1">Dftn</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="petri_df.html#D8" target="_self" onmouseover="rs('petri_df/D8')" onmouseout="rh()">Def5</a>, <a class="txt" href="#E1:24"><span class="lab"><font color="Green" title="E11">A3</font></span></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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