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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><br/>  for <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">F</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="polnot_1.html#K19" title="POLNOT_1:func.19">Polish-expression-hierarchy</a> (<font color="Maroon" title="c1">T</font>,<font color="Olive" title="b1">A</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>) holds  <font color="Maroon" title="c1">T</font> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <font color="Olive" title="b3">F</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <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="Olive" title="b1">A</font>,<font color="Olive" title="b2">n</font>)</span>)</span> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <span class="p1">(<span class="default"><a href="polnot_1.html#K32" title="POLNOT_1:func.32">Polish-arity</a> <font color="Olive" title="b3">F</font></span>)</span></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">  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">F</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <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="Olive" title="b1">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>) holds  <font color="Maroon" title="c1">T</font> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <font color="Olive" title="b2">F</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <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="Olive" title="b1">n</font>)</span>)</span> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <span class="p1">(<span class="default"><a href="polnot_1.html#K32" title="POLNOT_1:func.32">Polish-arity</a> <font color="Olive" title="b2">F</font></span>)</span></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">F</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <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="c3">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>) holds  <font color="Maroon" title="c1">T</font> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <font color="Olive" title="b1">F</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <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="c3">n</font>)</span>)</span> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <span class="p1">(<span class="default"><a href="polnot_1.html#K32" title="POLNOT_1:func.32">Polish-arity</a> <font color="Olive" title="b1">F</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">F</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <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="c3">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</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="c1">T</font> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <font color="Maroon" title="c4">F</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <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="c3">n</font>)</span>)</span> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <span class="p1">(<span class="default"><a href="polnot_1.html#K32" title="POLNOT_1:func.32">Polish-arity</a> <font color="Maroon" title="c4">F</font></span>)</span></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="c3">n</font>);<br/>
<a NAME="E1:139"/>
<font color="Maroon" title="c4">F</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="c3">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>)
 
;<br/>
<a NAME="E2:139"/><span class="kw">then </span>
<font color="Maroon" title="c4">F</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="c3">n</font>)</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polnot_1.html#T23" target="_self" onmouseover="rs('polnot_1/T23')" onmouseout="rh()">Th23</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">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="c7">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="E4:139"/><span class="lab"><font color="Green" title="E80">A2</font></span>: 
<font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">t</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c7">u</font>
 <span class="kw">and </span><br/><a NAME="E5:139"/><span class="lab"><font color="Green" title="E81">A3</font></span>: 
<font color="Maroon" title="c7">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <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="c3">n</font>)</span>)</span> <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="c6">t</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polnot_1.html#D19" target="_self" onmouseover="rs('polnot_1/D19')" onmouseout="rh()">Def19</a></span>;<br/>
<span class="kw">thus </span><a NAME="E6:139"/>
<font color="Maroon" title="c1">T</font> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <font color="Maroon" title="c4">F</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <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="c3">n</font>)</span>)</span> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <span class="p1">(<span class="default"><a href="polnot_1.html#K32" title="POLNOT_1:func.32">Polish-arity</a> <font color="Maroon" title="c4">F</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:139"><span class="lab"><font color="Green" title="E80">A2</font></span></a>, <a class="txt" href="#E5:139"><span class="lab"><font color="Green" title="E81">A3</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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