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<span class="kw">let </span><font color="Maroon" title="c1">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">A</font> being    <a href="polnot_1.html#M1" title="POLNOT_1:mode.1">Polish-arity-function</a> of <font color="Maroon" title="c1">T</font> holds   <a href="polnot_1.html#K21" title="POLNOT_1:func.21">Polish-WFF-set</a> (<font color="Maroon" title="c1">T</font>,<font color="Olive" title="b1">A</font>) is <font color="Maroon" title="c1">T</font> <a href="polnot_1.html#V6" title="POLNOT_1:attr.6">-headed</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be    <a href="polnot_1.html#M1" title="POLNOT_1:mode.1">Polish-arity-function</a> of <font color="Maroon" title="c1">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#K21" title="POLNOT_1:func.21">Polish-WFF-set</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>) is <font color="Maroon" title="c1">T</font> <a href="polnot_1.html#V6" title="POLNOT_1:attr.6">-headed</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">p</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="polnot_1.html#D21" target="_self" onmouseover="rs('polnot_1/D21')" onmouseout="rh()">POLNOT_1:def 21</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">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="polnot_1.html#K21" title="POLNOT_1:func.21">Polish-WFF-set</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>) implies <font color="Maroon" title="c3">p</font> is <font color="Maroon" title="c1">T</font> <a href="polnot_1.html#V5" title="POLNOT_1:attr.5">-headed</a>  )</span><br/>





<span class="kw">assume </span><a NAME="E1:132"/>
<font color="Maroon" title="c3">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="polnot_1.html#K21" title="POLNOT_1:func.21">Polish-WFF-set</a> (<font color="Maroon" title="c1">T</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="c3">p</font> is <font color="Maroon" title="c1">T</font> <a href="polnot_1.html#V5" title="POLNOT_1:attr.5">-headed</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:132"/><span class="lab"><font color="Green" title="E77">A3</font></span>: 
<font color="Maroon" title="c3">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="polnot_1.html#K19" title="POLNOT_1:func.19">Polish-expression-hierarchy</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">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">set </span><font color="Maroon" title="c5">U</font> =  <a href="polnot_1.html#K19" title="POLNOT_1:func.19">Polish-expression-hierarchy</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">n</font>);<br/>
<a NAME="E4:132"/>
<font color="Maroon" title="c3">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="polnot_1.html#K17" title="POLNOT_1:func.17">Polish-expression-layer</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>,<span class="p1">(<span class="default"><a href="polnot_1.html#K19" title="POLNOT_1:func.19">Polish-expression-hierarchy</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">n</font>)</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:132"><span class="lab"><font color="Green" title="E77">A3</font></span></a>, <a class="ref" href="polnot_1.html#T23" target="_self" onmouseover="rs('polnot_1/T23')" onmouseout="rh()">Th23</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:132"/>
<font color="Maroon" title="c3">p</font> is <font color="Maroon" title="c1">T</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#T21" target="_self" onmouseover="rs('polnot_1/T21')" onmouseout="rh()">Th21</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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