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<span class="kw">set </span><font color="Maroon" title="c3">f</font> =  <a href="polnot_1.html#K13" title="POLNOT_1:func.13">arity-from-list</a> <font color="Maroon" title="c2">B</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E2:122_1_1"/><span class="lab"><font color="Green" title="E70">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">T</font>
 <span class="kw">and </span><br/><a NAME="E3:122_1_1"/><span class="lab"><font color="Green" title="E71">A2</font></span>: 
 for <font color="Olive" title="b1">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">B</font> holds <br/> not <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polnot_1.html#T59" target="_self" onmouseover="rs('polnot_1/T59')" onmouseout="rh()">Th59</a></span>;<br/>
<a NAME="E4:122_1_1"/>
 for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  holds  not <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="122_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">given </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><a NAME="E2:122_1_1_1"/><span class="lab"><font color="Green" title="E72">A3</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</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"> contradiction</span><br/>

<a NAME="E3:122_1_1_1"/>
<font color="Maroon" title="c5">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:122_1_1_1"><span class="lab"><font color="Green" title="E72">A3</font></span></a>, <a class="ref" href="funct_1.html#D2" onmouseover="rs('funct_1/D2')" onmouseout="rh()">FUNCT_1:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:122_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:122_1_1"><span class="lab"><font color="Green" title="E71">A2</font></span></a>, <a class="txt" href="#E2:122_1_1_1"><span class="lab"><font color="Green" title="E72">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/>


</div><span class="kw">end;</span></div>
<a NAME="E5:122_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="polnot_1.html#K13" title="POLNOT_1:func.13">arity-from-list</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">a</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="ref" href="polnot_1.html#T30" target="_self" onmouseover="rs('polnot_1/T30')" onmouseout="rh()">Th30</a>, <a class="txt" href="#E2:122_1_1"><span class="lab"><font color="Green" title="E70">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:122_1_1"/>
 <a href="polnot_1.html#K13" title="POLNOT_1:func.13">arity-from-list</a> <font color="Maroon" title="c2">B</font> is    <a href="polnot_1.html#M1" title="POLNOT_1:mode.1">Polish-arity-function</a> of <font color="Maroon" title="c1">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:122_1_1"><span class="lab"><font color="Green" title="E70">A1</font></span></a>, <a class="ref" href="polnot_1.html#D18" target="_self" onmouseover="rs('polnot_1/D18')" onmouseout="rh()">Def18</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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