<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">P</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="pnproc_1.html#M2" title="PNPROC_1:mode.2">Petri_net</a> of <font color="Maroon" title="c1">P</font><br/> for <font color="Olive" title="b2">R1</font>, <font color="Olive" title="b3">R2</font>, <font color="Olive" title="b4">R3</font> being  <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">process</a> of <font color="Olive" title="b1">N</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Olive" title="b3">R2</font></span>)</span> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Olive" title="b4">R3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">R2</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Olive" title="b4">R3</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">N</font> be    <a href="pnproc_1.html#M2" title="PNPROC_1:mode.2">Petri_net</a> of <font color="Maroon" title="c1">P</font>; <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">R1</font>, <font color="Olive" title="b2">R2</font>, <font color="Olive" title="b3">R3</font> being  <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">process</a> of <font color="Maroon" title="c2">N</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Olive" title="b2">R2</font></span>)</span> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Olive" title="b3">R3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">R2</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Olive" title="b3">R3</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">R1</font>, <font color="Maroon" title="c4">R2</font>, <font color="Maroon" title="c5">R3</font> be   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">process</a> of <font color="Maroon" title="c2">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R3</font></span>)</span></span><br/>









<span class="kw">thus </span><a NAME="E1:81"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R3</font></span>)</span>
  <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</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="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R3</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R3</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="81_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R3</font> or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R3</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:81_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R3</font>
 ; <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="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R3</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">C1</font>, <font color="Maroon" title="c8">C2</font> being   <a href="pnproc_1.html#NM5" title="PNPROC_1:NM.5">firing-sequence</a> of <font color="Maroon" title="c2">N</font><span class="kw"> such that </span><br/><a NAME="E3:81_1"/><span class="lab"><font color="Green" title="E46">A1</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">C1</font> <a href="pre_poly.html#K1" title="PRE_POLY:func.1">^</a> <font color="Maroon" title="c8">C2</font>
 <span class="kw">and </span><br/><a NAME="E4:81_1"/><span class="lab"><font color="Green" title="E47">A2</font></span>: 
<font color="Maroon" title="c7">C1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c4">R2</font>
 <span class="kw">and </span><br/><a NAME="E5:81_1"/><span class="lab"><font color="Green" title="E48">A3</font></span>: 
<font color="Maroon" title="c8">C2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">R3</font>
 ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c9">fs1</font>, <font color="Maroon" title="c10">fs2</font> being   <a href="pnproc_1.html#NM5" title="PNPROC_1:NM.5">firing-sequence</a> of <font color="Maroon" title="c2">N</font><span class="kw"> such that </span><br/><a NAME="E7:81_1"/><span class="lab"><font color="Green" title="E49">A4</font></span>: 
<font color="Maroon" title="c7">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">fs1</font> <a href="pre_poly.html#K1" title="PRE_POLY:func.1">^</a> <font color="Maroon" title="c10">fs2</font>
 <span class="kw">and </span><br/><a NAME="E8:81_1"/><span class="lab"><font color="Green" title="E50">A5</font></span>: 
<font color="Maroon" title="c9">fs1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font>
 <span class="kw">and </span><br/><a NAME="E9:81_1"/><span class="lab"><font color="Green" title="E51">A6</font></span>: 
<font color="Maroon" title="c10">fs2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">R2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:81_1"><span class="lab"><font color="Green" title="E47">A2</font></span></a></span>;<br/>
<a NAME="E10:81_1"/><span class="lab"><font color="Green" title="E52">A7</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">fs1</font> <a href="pre_poly.html#K1" title="PRE_POLY:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">fs2</font> <a href="pre_poly.html#K1" title="PRE_POLY:func.1">^</a> <font color="Maroon" title="c8">C2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:81_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E7:81_1"><span class="lab"><font color="Green" title="E49">A4</font></span></a>, <a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c11">C3</font> being   <a href="pnproc_1.html#NM5" title="PNPROC_1:NM.5">firing-sequence</a> of <font color="Maroon" title="c2">N</font><span class="kw"> such that </span><br/><a NAME="E12:81_1"/><span class="lab"><font color="Green" title="E53">A8</font></span>: 
<font color="Maroon" title="c11">C3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">fs2</font> <a href="pre_poly.html#K1" title="PRE_POLY:func.1">^</a> <font color="Maroon" title="c8">C2</font>
 <span class="kw">and </span><br/><a NAME="E13:81_1"/><span class="lab"><font color="Green" title="E54">A9</font></span>: 
<font color="Maroon" title="c10">fs2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">R2</font>
 <span class="kw">and </span><br/><a NAME="E14:81_1"/><span class="lab"><font color="Green" title="E55">A10</font></span>: 
<font color="Maroon" title="c8">C2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">R3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:81_1"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="txt" href="#E9:81_1"><span class="lab"><font color="Green" title="E51">A6</font></span></a></span>;<br/>
<a NAME="E15:81_1"/>
<font color="Maroon" title="c11">C3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:81_1"><span class="lab"><font color="Green" title="E53">A8</font></span></a>, <a class="txt" href="#E13:81_1"><span class="lab"><font color="Green" title="E54">A9</font></span></a>, <a class="txt" href="#E14:81_1"><span class="lab"><font color="Green" title="E55">A10</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E16:81_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:81_1"><span class="lab"><font color="Green" title="E50">A5</font></span></a>, <a class="txt" href="#E10:81_1"><span class="lab"><font color="Green" title="E52">A7</font></span></a>, <a class="txt" href="#E12:81_1"><span class="lab"><font color="Green" title="E53">A8</font></span></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/>


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

<span class="kw">let </span><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R3</font></span>)</span> or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R3</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:81"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R3</font></span>)</span>
 ; <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="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R3</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">C1</font>, <font color="Maroon" title="c8">C2</font> being   <a href="pnproc_1.html#NM5" title="PNPROC_1:NM.5">firing-sequence</a> of <font color="Maroon" title="c2">N</font><span class="kw"> such that </span><br/><a NAME="E4:81"/><span class="lab"><font color="Green" title="E46">A11</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">C1</font> <a href="pre_poly.html#K1" title="PRE_POLY:func.1">^</a> <font color="Maroon" title="c8">C2</font>
 <span class="kw">and </span><br/><a NAME="E5:81"/><span class="lab"><font color="Green" title="E47">A12</font></span>: 
<font color="Maroon" title="c7">C1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font>
 <span class="kw">and </span><br/><a NAME="E6:81"/><span class="lab"><font color="Green" title="E48">A13</font></span>: 
<font color="Maroon" title="c8">C2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R3</font>
 ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c9">fs1</font>, <font color="Maroon" title="c10">fs2</font> being   <a href="pnproc_1.html#NM5" title="PNPROC_1:NM.5">firing-sequence</a> of <font color="Maroon" title="c2">N</font><span class="kw"> such that </span><br/><a NAME="E8:81"/><span class="lab"><font color="Green" title="E49">A14</font></span>: 
<font color="Maroon" title="c8">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">fs1</font> <a href="pre_poly.html#K1" title="PRE_POLY:func.1">^</a> <font color="Maroon" title="c10">fs2</font>
 <span class="kw">and </span><br/><a NAME="E9:81"/><span class="lab"><font color="Green" title="E50">A15</font></span>: 
<font color="Maroon" title="c9">fs1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">R2</font>
 <span class="kw">and </span><br/><a NAME="E10:81"/><span class="lab"><font color="Green" title="E51">A16</font></span>: 
<font color="Maroon" title="c10">fs2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">R3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:81"><span class="lab"><font color="Green" title="E48">A13</font></span></a></span>;<br/>
<a NAME="E11:81"/><span class="lab"><font color="Green" title="E52">A17</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">C1</font> <a href="pre_poly.html#K1" title="PRE_POLY:func.1">^</a> <font color="Maroon" title="c9">fs1</font></span>)</span> <a href="pre_poly.html#K1" title="PRE_POLY:func.1">^</a> <font color="Maroon" title="c10">fs2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:81"><span class="lab"><font color="Green" title="E46">A11</font></span></a>, <a class="txt" href="#E8:81"><span class="lab"><font color="Green" title="E49">A14</font></span></a>, <a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c11">C</font> being   <a href="pnproc_1.html#NM5" title="PNPROC_1:NM.5">firing-sequence</a> of <font color="Maroon" title="c2">N</font><span class="kw"> such that </span><br/><a NAME="E13:81"/><span class="lab"><font color="Green" title="E53">A18</font></span>: 
<font color="Maroon" title="c11">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">C1</font> <a href="pre_poly.html#K1" title="PRE_POLY:func.1">^</a> <font color="Maroon" title="c9">fs1</font>
 <span class="kw">and </span><br/><a NAME="E14:81"/><span class="lab"><font color="Green" title="E54">A19</font></span>: 
<font color="Maroon" title="c7">C1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font>
 <span class="kw">and </span><br/><a NAME="E15:81"/><span class="lab"><font color="Green" title="E55">A20</font></span>: 
<font color="Maroon" title="c9">fs1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">R2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:81"><span class="lab"><font color="Green" title="E47">A12</font></span></a>, <a class="txt" href="#E9:81"><span class="lab"><font color="Green" title="E50">A15</font></span></a></span>;<br/>
<a NAME="E16:81"/>
<font color="Maroon" title="c11">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c4">R2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:81"><span class="lab"><font color="Green" title="E53">A18</font></span></a>, <a class="txt" href="#E14:81"><span class="lab"><font color="Green" title="E54">A19</font></span></a>, <a class="txt" href="#E15:81"><span class="lab"><font color="Green" title="E55">A20</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:81"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:81"><span class="lab"><font color="Green" title="E51">A16</font></span></a>, <a class="txt" href="#E11:81"><span class="lab"><font color="Green" title="E52">A17</font></span></a>, <a class="txt" href="#E13:81"><span class="lab"><font color="Green" title="E53">A18</font></span></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/>


</div>
