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<span class="kw">let </span><font color="Maroon" title="c1">x</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"> ( <font color="Maroon" title="c1">x</font> is  <a href="numpoly1.html#V1" title="NUMPOLY1:attr.1">triangular</a>  implies <font color="Maroon" title="c1">x</font> is 3 <a href="numpoly1.html#V2" title="NUMPOLY1:attr.2">-gonal</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:79_2_1"/>
<font color="Maroon" title="c1">x</font> is  <a href="numpoly1.html#V1" title="NUMPOLY1:attr.1">triangular</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="c1">x</font> is 3 <a href="numpoly1.html#V2" title="NUMPOLY1:attr.2">-gonal</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:79_2_1"/><span class="lab"><font color="Green" title="E42">A1</font></span>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numpoly1.html#K1" title="NUMPOLY1:func.1">Triangle</a> <font color="Maroon" title="c2">n</font>
 ;<br/>
<a NAME="E4:79_2_1"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numpoly1.html#K2" title="NUMPOLY1:func.2">Polygon</a> (3,<font color="Maroon" title="c2">n</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:79_2_1"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="numpoly1.html#T40" target="_self" onmouseover="rs('numpoly1/T40')" onmouseout="rh()">Th40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:79_2_1"/>
<font color="Maroon" title="c1">x</font> is 3 <a href="numpoly1.html#V2" title="NUMPOLY1:attr.2">-gonal</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"> verum</span><br/>


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