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<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ] <span class="kw">means </span> ex <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="c1">T</font> ex <font color="Olive" title="b2">u</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">T</font> <a href="polnot_1.html#K5" title="POLNOT_1:func.5">*</a>  st <br/>( $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">t</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b2">u</font> &amp; <font color="Olive" title="b2">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">U</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="polnot_1.html#K14" title="POLNOT_1:func.14">.</a> <font color="Olive" title="b1">t</font></span>)</span> );<br/>
<span class="kw">set </span><font color="Maroon" title="c4">X</font> =  <a href="polnot_1.html#K6" title="POLNOT_1:func.6">Polish-expression-layer</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">U</font>);<br/>
<span class="kw">let </span><font color="Maroon" title="c5">Y</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="polnot_1.html#K5" title="POLNOT_1:func.5">*</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="c5">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polnot_1.html#K6" title="POLNOT_1:func.6">Polish-expression-layer</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">U</font>) iff  for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Y</font> iff  ex <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="c1">T</font> ex <font color="Olive" title="b3">u</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">T</font> <a href="polnot_1.html#K5" title="POLNOT_1:func.5">*</a>  st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">t</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b3">u</font> &amp; <font color="Olive" title="b3">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">U</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="polnot_1.html#K14" title="POLNOT_1:func.14">.</a> <font color="Olive" title="b2">t</font></span>)</span> ) ) )</span><br/>

<a NAME="E1:84_1_1"/><span class="lab"><font color="Green" title="E52">A1</font></span>: 
 for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K6" title="POLNOT_1:func.6">Polish-expression-layer</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">U</font>) iff <font color="Maroon">S<sub>1</sub></font>[<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="84_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">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="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K6" title="POLNOT_1:func.6">Polish-expression-layer</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">U</font>) iff <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">a</font>] )</span><br/>

<span class="kw">thus </span><a NAME="E1:84_1_1_1"/>
( <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K6" title="POLNOT_1:func.6">Polish-expression-layer</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">U</font>) implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">a</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">S<sub>1</sub></font>[<font color="Maroon" title="c6">a</font>] implies <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K6" title="POLNOT_1:func.6">Polish-expression-layer</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">U</font>) )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="84_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:84_1_1_1_1"/>
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K6" title="POLNOT_1:func.6">Polish-expression-layer</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">U</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">S<sub>1</sub></font>[<font color="Maroon" title="c6">a</font>]</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">t</font>, <font color="Maroon" title="c8">q</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>, <font color="Maroon" title="c9">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:84_1_1_1_1"/><span class="lab"><font color="Green" title="E53">A3</font></span>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">t</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c8">q</font>
 <span class="kw">and </span><br/><a NAME="E4:84_1_1_1_1"/><span class="lab"><font color="Green" title="E54">A4</font></span>: 
<font color="Maroon" title="c7">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">T</font>
 <span class="kw">and </span><br/><a NAME="E5:84_1_1_1_1"/><span class="lab"><font color="Green" title="E55">A5</font></span>: 
<font color="Maroon" title="c9">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">t</font>
 <span class="kw">and </span><br/><a NAME="E6:84_1_1_1_1"/><span class="lab"><font color="Green" title="E56">A6</font></span>: 
<font color="Maroon" title="c8">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">U</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Maroon" title="c9">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polnot_1.html#D6" target="_self" onmouseover="rs('polnot_1/D6')" onmouseout="rh()">Def6</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">t1</font> = <font color="Maroon" title="c7">t</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">T</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:84_1_1_1_1"><span class="lab"><font color="Green" title="E54">A4</font></span></a></span>;<br/>
<a NAME="E8:84_1_1_1_1"/>
<font color="Maroon" title="c3">U</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Maroon" title="c9">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">T</font> <a href="polnot_1.html#K5" title="POLNOT_1:func.5">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polnot_1.html#T14" target="_self" onmouseover="rs('polnot_1/T14')" onmouseout="rh()">Th14</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">q1</font> = <font color="Maroon" title="c8">q</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">T</font> <a href="polnot_1.html#K5" title="POLNOT_1:func.5">*</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:84_1_1_1_1"><span class="lab"><font color="Green" title="E56">A6</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c10">t1</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">  ex <font color="Olive" title="b1">u</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">T</font> <a href="polnot_1.html#K5" title="POLNOT_1:func.5">*</a>  st <br/>( <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">t1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b1">u</font> &amp; <font color="Olive" title="b1">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">U</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="polnot_1.html#K14" title="POLNOT_1:func.14">.</a> <font color="Maroon" title="c10">t1</font></span>)</span> )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c11">q1</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="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">t1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c11">q1</font> &amp; <font color="Maroon" title="c11">q1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">U</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="polnot_1.html#K14" title="POLNOT_1:func.14">.</a> <font color="Maroon" title="c10">t1</font></span>)</span> )</span><br/>

<span class="kw">thus </span><a NAME="E10:84_1_1_1_1"/>
( <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">t1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c11">q1</font> &amp; <font color="Maroon" title="c11">q1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">U</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="polnot_1.html#K14" title="POLNOT_1:func.14">.</a> <font color="Maroon" title="c10">t1</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:84_1_1_1_1"><span class="lab"><font color="Green" title="E53">A3</font></span></a>, <a class="txt" href="#E5:84_1_1_1_1"><span class="lab"><font color="Green" title="E55">A5</font></span></a>, <a class="txt" href="#E6:84_1_1_1_1"><span class="lab"><font color="Green" title="E56">A6</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/>


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

<span class="kw">assume </span><a NAME="E2:84_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">a</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="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K6" title="POLNOT_1:func.6">Polish-expression-layer</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">U</font>)</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">t</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">T</font>, <font color="Maroon" title="c8">u</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">T</font> <a href="polnot_1.html#K5" title="POLNOT_1:func.5">*</a> <span class="kw"> such that </span><br/><a NAME="E4:84_1_1_1"/><span class="lab"><font color="Green" title="E53">A10</font></span>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">t</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c8">u</font>
 <span class="kw">and </span><br/><a NAME="E5:84_1_1_1"/><span class="lab"><font color="Green" title="E54">A11</font></span>: 
<font color="Maroon" title="c8">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">U</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="polnot_1.html#K14" title="POLNOT_1:func.14">.</a> <font color="Maroon" title="c7">t</font></span>)</span>
 ;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">n</font> = <font color="Maroon" title="c2">A</font> <a href="polnot_1.html#K14" title="POLNOT_1:func.14">.</a> <font color="Maroon" title="c7">t</font>;<br/>
<a NAME="E6:84_1_1_1"/>
<font color="Maroon" title="c1">T</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">T</font> <a href="polnot_1.html#K5" title="POLNOT_1:func.5">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polnot_1.html#T9" target="_self" onmouseover="rs('polnot_1/T9')" onmouseout="rh()">Th9</a></span>;<br/>
<a NAME="E7:84_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">T</font> <a href="polnot_1.html#K5" title="POLNOT_1:func.5">*</a> 
 
;<br/>
<a NAME="E8:84_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">T</font> <a href="polnot_1.html#K5" title="POLNOT_1:func.5">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:84_1_1_1"><span class="lab"><font color="Green" title="E53">A10</font></span></a>, <a class="ref" href="polnot_1.html#T12" target="_self" onmouseover="rs('polnot_1/T12')" onmouseout="rh()">Th12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:84_1_1_1"/>
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K6" title="POLNOT_1:func.6">Polish-expression-layer</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">U</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:84_1_1_1"><span class="lab"><font color="Green" title="E53">A10</font></span></a>, <a class="txt" href="#E5:84_1_1_1"><span class="lab"><font color="Green" title="E54">A11</font></span></a>, <a class="ref" href="polnot_1.html#D6" target="_self" onmouseover="rs('polnot_1/D6')" onmouseout="rh()">Def6</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="E2:84_1_1"/>
(  <a href="polnot_1.html#K6" title="POLNOT_1:func.6">Polish-expression-layer</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">U</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Y</font> implies  for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Y</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">a</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">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Y</font> iff  ex <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="c1">T</font> ex <font color="Olive" title="b3">u</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">T</font> <a href="polnot_1.html#K5" title="POLNOT_1:func.5">*</a>  st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">t</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b3">u</font> &amp; <font color="Olive" title="b3">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">U</font> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="polnot_1.html#K14" title="POLNOT_1:func.14">.</a> <font color="Olive" title="b2">t</font></span>)</span> ) ) ) implies <font color="Maroon" title="c5">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polnot_1.html#K6" title="POLNOT_1:func.6">Polish-expression-layer</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">U</font>) )</span><br/>

<span class="kw">assume </span><a NAME="E3:84_1_1"/><span class="lab"><font color="Green" title="E53">A20</font></span>: 
 for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Y</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">a</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="c5">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polnot_1.html#K6" title="POLNOT_1:func.6">Polish-expression-layer</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">U</font>)</span><br/>

<span class="kw">thus </span><a NAME="E4:84_1_1"/>
 <a href="polnot_1.html#K6" title="POLNOT_1:func.6">Polish-expression-layer</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">U</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Y</font>
 <span class="kw">from</span> <span class="lab"><a class="ref" href="xboole_0.html#S2" onmouseover="rs('xboole_0/S2')" onmouseout="rh()">XBOOLE_0:sch 2</a>(<a class="txt" href="#E1:84_1_1"><span class="lab"><font color="Green" title="E52">A1</font></span></a>, <a class="txt" href="#E3:84_1_1"><span class="lab"><font color="Green" title="E53">A20</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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