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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   non  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  <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">E</font> being    <a href="polnot_1.html#M1" title="POLNOT_1:mode.1">Polish-arity-function</a> of <font color="Maroon" title="c1">L</font><br/>  for <font color="Olive" title="b2">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">g</font> being   <a href="polnot_1.html#NM7" title="POLNOT_1:NM.7">Polish-recursion-function</a> of <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">D</font>  ex <font color="Olive" title="b4">J</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polnot_1.html#K21" title="POLNOT_1:func.21">Polish-WFF-set</a> (<font color="Maroon" title="c1">L</font>,<font color="Olive" title="b1">E</font>)</span>)</span> ex <font color="Olive" title="b5">H</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b4">J</font>,<font color="Olive" title="b2">D</font> st <br/>( <font color="Olive" title="b4">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polnot_1.html#K19" title="POLNOT_1:func.19">Polish-expression-hierarchy</a> (<font color="Maroon" title="c1">L</font>,<font color="Olive" title="b1">E</font>,<a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>) &amp; <font color="Olive" title="b5">H</font> is <font color="Olive" title="b3">g</font> <a href="polnot_1.html#V9" title="POLNOT_1:attr.9">-recursive</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">E</font> be    <a href="polnot_1.html#M1" title="POLNOT_1:mode.1">Polish-arity-function</a> of <font color="Maroon" title="c1">L</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">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">g</font> being   <a href="polnot_1.html#NM7" title="POLNOT_1:NM.7">Polish-recursion-function</a> of <font color="Maroon" title="c2">E</font>,<font color="Olive" title="b1">D</font>  ex <font color="Olive" title="b3">J</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polnot_1.html#K21" title="POLNOT_1:func.21">Polish-WFF-set</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>)</span>)</span> ex <font color="Olive" title="b4">H</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b3">J</font>,<font color="Olive" title="b1">D</font> st <br/>( <font color="Olive" title="b3">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polnot_1.html#K19" title="POLNOT_1:func.19">Polish-expression-hierarchy</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>) &amp; <font color="Olive" title="b4">H</font> is <font color="Olive" title="b2">g</font> <a href="polnot_1.html#V9" title="POLNOT_1:attr.9">-recursive</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">D</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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">g</font> being   <a href="polnot_1.html#NM7" title="POLNOT_1:NM.7">Polish-recursion-function</a> of <font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c3">D</font>  ex <font color="Olive" title="b2">J</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polnot_1.html#K21" title="POLNOT_1:func.21">Polish-WFF-set</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>)</span>)</span> ex <font color="Olive" title="b3">H</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b2">J</font>,<font color="Maroon" title="c3">D</font> st <br/>( <font color="Olive" title="b2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polnot_1.html#K19" title="POLNOT_1:func.19">Polish-expression-hierarchy</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>) &amp; <font color="Olive" title="b3">H</font> is <font color="Olive" title="b1">g</font> <a href="polnot_1.html#V9" title="POLNOT_1:attr.9">-recursive</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">g</font> be   <a href="polnot_1.html#NM7" title="POLNOT_1:NM.7">Polish-recursion-function</a> of <font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c3">D</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">J</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polnot_1.html#K21" title="POLNOT_1:func.21">Polish-WFF-set</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>)</span>)</span> ex <font color="Olive" title="b2">H</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">J</font>,<font color="Maroon" title="c3">D</font> st <br/>( <font color="Olive" title="b1">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polnot_1.html#K19" title="POLNOT_1:func.19">Polish-expression-hierarchy</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>) &amp; <font color="Olive" title="b2">H</font> is <font color="Maroon" title="c4">g</font> <a href="polnot_1.html#V9" title="POLNOT_1:attr.9">-recursive</a>  )</span><br/>







<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ) <span class="kw">-&gt; </span>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  = <font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">$1,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">J</font> =  <a href="polnot_1.html#K19" title="POLNOT_1:func.19">Polish-expression-hierarchy</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>);<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">J</font> =  <a href="polnot_1.html#K19" title="POLNOT_1:func.19">Polish-expression-hierarchy</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>) as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polnot_1.html#K21" title="POLNOT_1:func.21">Polish-WFF-set</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>)</span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="polnot_1.html#T26" target="_self" onmouseover="rs('polnot_1/T26')" onmouseout="rh()">Th26</a></span>;<br/>
<a NAME="E2:157"/><span class="lab"><font color="Green" title="E85">A1</font></span>: 
 for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">J</font> holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">a</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">D</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="157_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c7">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="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">J</font> implies <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c7">a</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">D</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:157_1"/>
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">J</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">H<sub>1</sub></font>(<font color="Maroon" title="c7">a</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">D</font></span><br/>

<a NAME="E2:157_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E86">A6</font></span>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K7" title="POLNOT_1:func.7">Polish-atoms</a> (<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#D9" target="_self" onmouseover="rs('polnot_1/D9')" onmouseout="rh()">Def9</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">t</font> = <font color="Maroon" title="c7">a</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="ref" href="polnot_1.html#D7" target="_self" onmouseover="rs('polnot_1/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">p</font> =  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <font color="Maroon" title="c3">D</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">b</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">t</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <font color="Maroon" title="c3">D</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<a NAME="E4:157_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <font color="Maroon" title="c3">D</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">E</font> <a href="polnot_1.html#K14" title="POLNOT_1:func.14">.</a> <font color="Maroon" title="c8">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:157_1"><span class="lab"><font color="Green" title="E86">A6</font></span></a>, <a class="ref" href="polnot_1.html#D7" target="_self" onmouseover="rs('polnot_1/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<a NAME="E5:157_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">t</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <font color="Maroon" title="c3">D</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K37" title="POLNOT_1:func.37">Polish-recursion-domain</a> (<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c3">D</font>)
 
;<br/>
<span class="kw">hence </span><a NAME="E6:157_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c7">a</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">D</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T5" onmouseover="rs('funct_2/T5')" onmouseout="rh()">FUNCT_2:5</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">consider </span><font color="Maroon" title="c7">H</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c3">D</font><span class="kw"> such that </span><br/><a NAME="E4:157"/><span class="lab"><font color="Green" title="E86">A9</font></span>: 
 for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">J</font> holds <br/><font color="Maroon" title="c7">H</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">a</font>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="funct_2.html#S2" onmouseover="rs('funct_2/S2')" onmouseout="rh()">FUNCT_2:sch 2</a>(<a class="txt" href="#E2:157"><span class="lab"><font color="Green" title="E85">A1</font></span></a>);<br/></span>
<span class="kw">take </span>
<font color="Maroon" title="c6">J</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">H</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c3">D</font> st <br/>( <font color="Maroon" title="c6">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polnot_1.html#K19" title="POLNOT_1:func.19">Polish-expression-hierarchy</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>) &amp; <font color="Olive" title="b1">H</font> is <font color="Maroon" title="c4">g</font> <a href="polnot_1.html#V9" title="POLNOT_1:attr.9">-recursive</a>  )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c7">H</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">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polnot_1.html#K19" title="POLNOT_1:func.19">Polish-expression-hierarchy</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>) &amp; <font color="Maroon" title="c7">H</font> is <font color="Maroon" title="c4">g</font> <a href="polnot_1.html#V9" title="POLNOT_1:attr.9">-recursive</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E5:157"/>
<font color="Maroon" title="c6">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polnot_1.html#K19" title="POLNOT_1:func.19">Polish-expression-hierarchy</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</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="c7">H</font> is <font color="Maroon" title="c4">g</font> <a href="polnot_1.html#V9" title="POLNOT_1:attr.9">-recursive</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c8">F</font> be   <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="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="polnot_1.html#D43" target="_self" onmouseover="rs('polnot_1/D43')" onmouseout="rh()">POLNOT_1:def 43</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="c8">F</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">J</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="polnot_1.html#K35" title="POLNOT_1:func.35">Polish-WFF-args</a> <font color="Maroon" title="c8">F</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">J</font> implies <font color="Maroon" title="c7">H</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="polnot_1.html#K15" title="POLNOT_1:func.15">-head</a> <font color="Maroon" title="c8">F</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">H</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p3">(<span class="default"><a href="polnot_1.html#K35" title="POLNOT_1:func.35">Polish-WFF-args</a> <font color="Maroon" title="c8">F</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E6:157"/><span class="lab"><font color="Green" title="E87">A10</font></span>: 
<font color="Maroon" title="c8">F</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">J</font>
 <span class="kw">and </span><br/><a NAME="E7:157"/>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="polnot_1.html#K35" title="POLNOT_1:func.35">Polish-WFF-args</a> <font color="Maroon" title="c8">F</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">J</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="c7">H</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="polnot_1.html#K15" title="POLNOT_1:func.15">-head</a> <font color="Maroon" title="c8">F</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">H</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p3">(<span class="default"><a href="polnot_1.html#K35" title="POLNOT_1:func.35">Polish-WFF-args</a> <font color="Maroon" title="c8">F</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><br/>

<a NAME="E8:157"/><span class="lab"><font color="Green" title="E88">A12</font></span>: 
<font color="Maroon" title="c8">F</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="polnot_1.html#K7" title="POLNOT_1:func.7">Polish-atoms</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:157"><span class="lab"><font color="Green" title="E87">A10</font></span></a>, <a class="ref" href="polnot_1.html#D9" target="_self" onmouseover="rs('polnot_1/D9')" onmouseout="rh()">Def9</a></span>;<br/>
<a NAME="E9:157"/><span class="kw">then </span>
<font color="Maroon" title="c8">F</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polnot_1.html#D7" target="_self" onmouseover="rs('polnot_1/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<a NAME="E10:157"/><span class="kw">then </span><span class="lab"><font color="Green" title="E89">A14</font></span>: 
 <a href="polnot_1.html#K29" title="POLNOT_1:func.29">Polish-WFF-head</a> <font color="Maroon" title="c8">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polnot_1.html#T53" target="_self" onmouseover="rs('polnot_1/T53')" onmouseout="rh()">Th53</a></span>;<br/>
<a NAME="E11:157"/><span class="kw">then </span>
 <a href="polnot_1.html#K31" title="POLNOT_1:func.31">Polish-arity</a> <font color="Maroon" title="c8">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:157"><span class="lab"><font color="Green" title="E88">A12</font></span></a>, <a class="ref" href="polnot_1.html#D7" target="_self" onmouseover="rs('polnot_1/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<a NAME="E12:157"/><span class="kw">then </span><span class="lab"><font color="Green" title="E90">A15</font></span>: 
 <a href="polnot_1.html#K35" title="POLNOT_1:func.35">Polish-WFF-args</a> <font color="Maroon" title="c8">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polnot_1.html#T61" target="_self" onmouseover="rs('polnot_1/T61')" onmouseout="rh()">Th61</a></span>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c7">H</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">F</font> = 
<font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="polnot_1.html#K15" title="POLNOT_1:func.15">-head</a> <font color="Maroon" title="c8">F</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:157"><span class="lab"><font color="Green" title="E86">A9</font></span></a>, <a class="txt" href="#E6:157"><span class="lab"><font color="Green" title="E87">A10</font></span></a>, <a class="txt" href="#E10:157"><span class="lab"><font color="Green" title="E89">A14</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="polnot_1.html#K15" title="POLNOT_1:func.15">-head</a> <font color="Maroon" title="c8">F</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">H</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p3">(<span class="default"><a href="polnot_1.html#K35" title="POLNOT_1:func.35">Polish-WFF-args</a> <font color="Maroon" title="c8">F</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:157"><span class="lab"><font color="Green" title="E90">A15</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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