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<span class="kw">set </span><font color="Maroon" title="c3">U</font> =  <a href="polnot_1.html#K20" title="POLNOT_1:func.20">Polish-expression-set</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>);<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E2:154_1_1"/><span class="lab"><font color="Green" title="E84">A1</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">L</font>
 <span class="kw">and </span><br/><a NAME="E3:154_1_1"/><span class="lab"><font color="Green" title="E85">A2</font></span>: 
<font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">L</font>
 <span class="kw">and </span><br/><a NAME="E4:154_1_1"/><span class="lab"><font color="Green" title="E86">A3</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D10" onmouseover="rs('zfmisc_1/D10')" onmouseout="rh()">ZFMISC_1:def 10</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">t</font> = <font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c7">u</font> = <font color="Maroon" title="c5">b</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">L</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:154_1_1"><span class="lab"><font color="Green" title="E84">A1</font></span></a>, <a class="txt" href="#E3:154_1_1"><span class="lab"><font color="Green" title="E85">A2</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">m</font> = <font color="Maroon" title="c2">E</font> <a href="polnot_1.html#K14" title="POLNOT_1:func.14">.</a> <font color="Maroon" title="c6">t</font>, <font color="Maroon" title="c9">n</font> = <font color="Maroon" title="c2">E</font> <a href="polnot_1.html#K14" title="POLNOT_1:func.14">.</a> <font color="Maroon" title="c7">u</font> as   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">v</font> = <span class="p1">(<span class="default"><a href="polnot_1.html#K12" title="POLNOT_1:func.12">Polish-operation</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c8">m</font>,<font color="Maroon" title="c6">t</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a>  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1">(<span class="default"><a href="polnot_1.html#K20" title="POLNOT_1:func.20">Polish-expression-set</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>)</span>)</span> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Maroon" title="c8">m</font> as   <a href="polnot_1.html#NM6" title="POLNOT_1:NM.6">Polish-WFF</a> of <font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="polnot_1.html#T39" target="_self" onmouseover="rs('polnot_1/T39')" onmouseout="rh()">Th39</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">w</font> = <span class="p1">(<span class="default"><a href="polnot_1.html#K12" title="POLNOT_1:func.12">Polish-operation</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c9">n</font>,<font color="Maroon" title="c7">u</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a>  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1">(<span class="default"><a href="polnot_1.html#K20" title="POLNOT_1:func.20">Polish-expression-set</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>)</span>)</span> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <font color="Maroon" title="c9">n</font> as   <a href="polnot_1.html#NM6" title="POLNOT_1:NM.6">Polish-WFF</a> of <font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="polnot_1.html#T39" target="_self" onmouseover="rs('polnot_1/T39')" onmouseout="rh()">Th39</a></span>;<br/>
<a NAME="E9:154_1_1"/>
(  <a href="polnot_1.html#K29" title="POLNOT_1:func.29">Polish-WFF-head</a> <font color="Maroon" title="c10">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">t</font> &amp;  <a href="polnot_1.html#K29" title="POLNOT_1:func.29">Polish-WFF-head</a> <font color="Maroon" title="c11">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">u</font> )
 
;<br/>
<span class="kw">hence </span><a NAME="E10:154_1_1"/>
 not  <a href="polnot_1.html#K20" title="POLNOT_1:func.20">Polish-expression-set</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>) is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:154_1_1"><span class="lab"><font color="Green" title="E86">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#D10" onmouseover="rs('zfmisc_1/D10')" onmouseout="rh()">ZFMISC_1:def 10</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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