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

<span class="kw">let </span><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</font> be   <a href="polnot_1.html#NM3" title="POLNOT_1:NM.3">Polish-language</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">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Olive" title="b1">n</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 <font color="Maroon" title="c2">T</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Olive" title="b1">n</font>  st <font color="Maroon" title="c1">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">T</font> &amp; <font color="Olive" title="b2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">t</font> holds <br/> <a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c1">S</font>,<font color="Olive" title="b1">n</font>,<font color="Olive" title="b2">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c2">T</font>,<font color="Olive" title="b1">n</font>,<font color="Olive" title="b3">t</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Maroon" title="c3">n</font><br/>  for <font color="Olive" title="b2">t</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">T</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Maroon" title="c3">n</font>  st <font color="Maroon" title="c1">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">T</font> &amp; <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">t</font> holds <br/> <a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">n</font>,<font color="Olive" title="b1">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">n</font>,<font color="Olive" title="b2">t</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">s</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Maroon" title="c3">n</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">  for <font color="Olive" title="b1">t</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">T</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Maroon" title="c3">n</font>  st <font color="Maroon" title="c1">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">T</font> &amp; <font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">t</font> holds <br/> <a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c4">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">n</font>,<font color="Olive" title="b1">t</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c5">t</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">T</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Maroon" title="c3">n</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"> ( <font color="Maroon" title="c1">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">T</font> &amp; <font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">t</font> implies  <a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c4">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c5">t</font>) )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:127"/><span class="lab"><font color="Green" title="E72">A1</font></span>: 
<font color="Maroon" title="c1">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">T</font>
 <span class="kw">and </span><br/><a NAME="E2:127"/><span class="lab"><font color="Green" title="E73">A2</font></span>: 
<font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">t</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="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c4">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c5">t</font>)</span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">p</font> =  <a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c4">s</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c7">q</font> =  <a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c5">t</font>);<br/>
<a NAME="E3:127"/><span class="lab"><font color="Green" title="E74">A4</font></span>: 
(  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c3">n</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c5">t</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c3">n</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polnot_1.html#D32" target="_self" onmouseover="rs('polnot_1/D32')" onmouseout="rh()">Def32</a></span>;<br/>
<a NAME="E4:127"/>
 for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c3">n</font> holds <br/><span class="p1">(<span class="default"><a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c5">t</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="127_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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="c8">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c3">n</font> implies <span class="p1">(<span class="default"><a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c5">t</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">a</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:127_1"/><span class="lab"><font color="Green" title="E75">A6</font></span>: 
<font color="Maroon" title="c8">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c3">n</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">(<span class="default"><a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c5">t</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">a</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">a</font> = <font color="Maroon" title="c8">a</font> as   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c10">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E4:127_1"/><span class="lab"><font color="Green" title="E76">A7</font></span>: 
<font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <span class="kw">and </span><br/><a NAME="E5:127_1"/><span class="lab"><font color="Green" title="E77">A8</font></span>: 
<span class="p1">(<span class="default"><a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K15" title="POLNOT_1:func.15">-head</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Maroon" title="c10">k</font></span>)</span> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <font color="Maroon" title="c4">s</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:127_1"><span class="lab"><font color="Green" title="E75">A6</font></span></a>, <a class="ref" href="polnot_1.html#D32" target="_self" onmouseover="rs('polnot_1/D32')" onmouseout="rh()">Def32</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c11">l</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E7:127_1"/><span class="lab"><font color="Green" title="E78">A9</font></span>: 
<font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">l</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <span class="kw">and </span><br/><a NAME="E8:127_1"/><span class="lab"><font color="Green" title="E79">A10</font></span>: 
<span class="p1">(<span class="default"><a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c5">t</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font> <a href="polnot_1.html#K15" title="POLNOT_1:func.15">-head</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">T</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Maroon" title="c11">l</font></span>)</span> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <font color="Maroon" title="c5">t</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:127_1"><span class="lab"><font color="Green" title="E75">A6</font></span></a>, <a class="ref" href="polnot_1.html#D32" target="_self" onmouseover="rs('polnot_1/D32')" onmouseout="rh()">Def32</a></span>;<br/>
<a NAME="E9:127_1"/><span class="lab"><font color="Green" title="E80">A11</font></span>: 
<font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Maroon" title="c11">l</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">T</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Maroon" title="c11">l</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:127"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="polnot_1.html#T17" target="_self" onmouseover="rs('polnot_1/T17')" onmouseout="rh()">Th17</a></span>;<br/>
<a NAME="E10:127_1"/>
<font color="Maroon" title="c11">l</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:127_1"><span class="lab"><font color="Green" title="E75">A6</font></span></a>, <a class="txt" href="#E7:127_1"><span class="lab"><font color="Green" title="E78">A9</font></span></a>, <a class="ref" href="finseq_1.html#T1" onmouseover="rs('finseq_1/T1')" onmouseout="rh()">FINSEQ_1:1</a></span>;<br/>
<a NAME="E11:127_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E81">A12</font></span>: 
( <font color="Maroon" title="c4">s</font> is <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Maroon" title="c11">l</font> <a href="polnot_1.html#V5" title="POLNOT_1:attr.5">-headed</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Maroon" title="c11">l</font></span>)</span> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <font color="Maroon" title="c4">s</font> is <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#V5" title="POLNOT_1:attr.5">-headed</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polnot_1.html#T57" target="_self" onmouseover="rs('polnot_1/T57')" onmouseout="rh()">Th57</a></span>;<br/>
<a NAME="E12:127_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E82">A14</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">T</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Maroon" title="c11">l</font></span>)</span> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <font color="Maroon" title="c5">t</font> is <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#V5" title="POLNOT_1:attr.5">-headed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:127"><span class="lab"><font color="Green" title="E73">A2</font></span></a>, <a class="txt" href="#E9:127_1"><span class="lab"><font color="Green" title="E80">A11</font></span></a>, <a class="ref" href="polnot_1.html#T55" target="_self" onmouseover="rs('polnot_1/T55')" onmouseout="rh()">Th55</a></span>;<br/>
<a NAME="E13:127_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Maroon" title="c10">k</font></span>)</span> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">T</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Maroon" title="c11">l</font></span>)</span> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <font color="Maroon" title="c5">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:127"><span class="lab"><font color="Green" title="E73">A2</font></span></a>, <a class="txt" href="#E4:127_1"><span class="lab"><font color="Green" title="E76">A7</font></span></a>, <a class="txt" href="#E7:127_1"><span class="lab"><font color="Green" title="E78">A9</font></span></a>, <a class="txt" href="#E9:127_1"><span class="lab"><font color="Green" title="E80">A11</font></span></a>, <a class="txt" href="#E11:127_1"><span class="lab"><font color="Green" title="E81">A12</font></span></a>, <a class="ref" href="polnot_1.html#T55" target="_self" onmouseover="rs('polnot_1/T55')" onmouseout="rh()">Th55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:127_1"/>
<span class="p1">(<span class="default"><a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c5">t</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:127"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="txt" href="#E5:127_1"><span class="lab"><font color="Green" title="E77">A8</font></span></a>, <a class="txt" href="#E8:127_1"><span class="lab"><font color="Green" title="E79">A10</font></span></a>, <a class="txt" href="#E12:127_1"><span class="lab"><font color="Green" title="E82">A14</font></span></a>, <a class="ref" href="polnot_1.html#T55" target="_self" onmouseover="rs('polnot_1/T55')" onmouseout="rh()">Th55</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">hence </span><a NAME="E5:127"/>
 <a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c4">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polnot_1.html#K28" title="POLNOT_1:func.28">decomp</a> (<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c5">t</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:127"><span class="lab"><font color="Green" title="E74">A4</font></span></a>, <a class="ref" href="funct_1.html#D11" onmouseover="rs('funct_1/D11')" onmouseout="rh()">FUNCT_1:def 11</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>
