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<span class="kw">let </span><font color="Maroon" title="c1">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"> ( <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies <span class="p1">(<span class="default"><a href="surrealn.html#K1" title="SURREALN:func.1">uInt</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="surreali.html#K12" title="SURREALI:func.12">"</a>  <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a> <a href="surrealn.html#K6" title="SURREALN:func.6">uReal</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">n</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:99"/><span class="lab"><font color="Green" title="E81">A1</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS: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"> <span class="p1">(<span class="default"><a href="surrealn.html#K1" title="SURREALN:func.1">uInt</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="surreali.html#K12" title="SURREALI:func.12">"</a>  <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a> <a href="surrealn.html#K6" title="SURREALN:func.6">uReal</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">n</font></span>)</span></span><br/>

<a NAME="E2:99"/><span class="kw">then </span>
(  <a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="surrealn.html#K1" title="SURREALN:func.1">uInt</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> &amp; <a href="surrealn.html#K1" title="SURREALN:func.1">uInt</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <a href="surrealn.html#K1" title="SURREALN:func.1">uInt</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surrealn.html#T9" target="_self" onmouseover="rs('surrealn/T9')" onmouseout="rh()">Th9</a>, <a class="ref" href="surrealn.html#D1" target="_self" onmouseover="rs('surrealn/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<a NAME="E3:99"/><span class="kw">then </span><span class="lab"><font color="Green" title="E82">A2</font></span>: 
 not <a href="surrealn.html#K1" title="SURREALN:func.1">uInt</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a>  <a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a> 
 
;<br/>
<a NAME="E4:99"/><span class="lab"><font color="Green" title="E83">A3</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="xcmplx_1.html#T106" onmouseover="rs('xcmplx_1/T106')" onmouseout="rh()">XCMPLX_1:106</a></span>;<br/>
<a NAME="E5:99"/>
( <a href="surrealn.html#K1" title="SURREALN:func.1">uInt</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="surrealn.html#K4" title="SURREALN:func.4">uDyadic</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font> &amp; <a href="surrealn.html#K4" title="SURREALN:func.4">uDyadic</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="surrealn.html#K6" title="SURREALN:func.6">uReal</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surrealn.html#D5" target="_self" onmouseover="rs('surrealn/D5')" onmouseout="rh()">Def5</a>, <a class="ref" href="surrealn.html#T46" target="_self" onmouseover="rs('surrealn/T46')" onmouseout="rh()">Th46</a></span>;<br/>
<a NAME="E6:99"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="surrealn.html#K1" title="SURREALN:func.1">uInt</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <span class="p1">(<span class="default"><a href="surrealn.html#K6" title="SURREALN:func.6">uReal</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a> <a href="surrealn.html#K6" title="SURREALN:func.6">uReal</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <a href="surrealn.html#K6" title="SURREALN:func.6">uReal</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surrealo.html#K1" title="SURREALO:func.1">1_No</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:99"><span class="lab"><font color="Green" title="E83">A3</font></span></a>, <a class="ref" href="surrealn.html#T57" target="_self" onmouseover="rs('surrealn/T57')" onmouseout="rh()">Th57</a>, <a class="ref" href="surrealn.html#T48" target="_self" onmouseover="rs('surrealn/T48')" onmouseout="rh()">Th48</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:99"/>
<span class="p1">(<span class="default"><a href="surrealn.html#K1" title="SURREALN:func.1">uInt</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="surreali.html#K12" title="SURREALI:func.12">"</a>  <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a> <a href="surrealn.html#K6" title="SURREALN:func.6">uReal</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="surreali.html#T42" onmouseover="rs('surreali/T42')" onmouseout="rh()">SURREALI:42</a>, <a class="txt" href="#E3:99"><span class="lab"><font color="Green" title="E82">A2</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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