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<span class="kw">let </span><font color="Maroon" title="c1">P</font> be   <a href="finseq_1.html#V4" title="FINSEQ_1:attr.4">FinSequence-membered</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">A</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">P</font>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a><br/>  for <font color="Olive" title="b2">Q</font> being   <a href="finseq_1.html#V4" title="FINSEQ_1:attr.4">FinSequence-membered</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b2">Q</font> is <font color="Olive" title="b1">A</font> <a href="polnot_1.html#V2" title="POLNOT_1:attr.2">-closed</a>  holds <br/> <a href="polnot_1.html#K11" title="POLNOT_1:func.11">Polish-expression-set</a> (<font color="Maroon" title="c1">P</font>,<font color="Olive" title="b1">A</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">Q</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">P</font>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">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">Q</font> being   <a href="finseq_1.html#V4" title="FINSEQ_1:attr.4">FinSequence-membered</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">Q</font> is <font color="Maroon" title="c2">A</font> <a href="polnot_1.html#V2" title="POLNOT_1:attr.2">-closed</a>  holds <br/> <a href="polnot_1.html#K11" title="POLNOT_1:func.11">Polish-expression-set</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">A</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">Q</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">Q</font> be   <a href="finseq_1.html#V4" title="FINSEQ_1:attr.4">FinSequence-membered</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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="c3">Q</font> is <font color="Maroon" title="c2">A</font> <a href="polnot_1.html#V2" title="POLNOT_1:attr.2">-closed</a>  implies  <a href="polnot_1.html#K11" title="POLNOT_1:func.11">Polish-expression-set</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">A</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">Q</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:61"/><span class="lab"><font color="Green" title="E42">A1</font></span>: 
<font color="Maroon" title="c3">Q</font> is <font color="Maroon" title="c2">A</font> <a href="polnot_1.html#V2" title="POLNOT_1:attr.2">-closed</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">  <a href="polnot_1.html#K11" title="POLNOT_1:func.11">Polish-expression-set</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">A</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">Q</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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"> (  not <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K11" title="POLNOT_1:func.11">Polish-expression-set</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">A</font>) or <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Q</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:61"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K11" title="POLNOT_1:func.11">Polish-expression-set</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">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="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Q</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E4:61"/><span class="lab"><font color="Green" title="E43">A2</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K10" title="POLNOT_1:func.10">Polish-expression-hierarchy</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">A</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polnot_1.html#T28" target="_self" onmouseover="rs('polnot_1/T28')" onmouseout="rh()">Th28</a></span>;<br/>
<span class="kw">thus </span><a NAME="E5:61"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="txt" href="#E4:61"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="polnot_1.html#T35" target="_self" onmouseover="rs('polnot_1/T35')" onmouseout="rh()">Th35</a>, <a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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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