<?xml version="1.0"?>
<div class="add">

<a NAME="E1:5_1_1"/>
1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="5_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:5_1_1_1"/>
1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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="E2:5_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">r</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">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">r</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E3:5_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="anproj10.html#D1" target="_self" onmouseover="rs('anproj10/D1')" onmouseout="rh()">Def01</a>, <a class="ref" href="xcmplx_1.html#T106" onmouseover="rs('xcmplx_1/T106')" onmouseout="rh()">XCMPLX_1:106</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">hence </span><a NAME="E2:5_1_1"/>
1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">r</font> is   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>   non  <a href="anproj10.html#V1" title="ANPROJ10:attr.1">unit</a>  <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="anproj10.html#D1" target="_self" onmouseover="rs('anproj10/D1')" onmouseout="rh()">Def01</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>
