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<span class="kw">let </span><font color="Maroon" title="c1">u</font>, <font color="Maroon" title="c2">u9</font>, <font color="Maroon" title="c3">v</font>, <font color="Maroon" title="c4">v9</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">u9</font> implies  ex <font color="Olive" title="b1">x</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">u9</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c4">v9</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">x</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">v9</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">v</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">u9</font></span>)</span>;<br/>
<span class="kw">assume </span><a NAME="E1:11"/>
<font color="Maroon" title="c1">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">u9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">x</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">u9</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c4">v9</font></span><br/>

<a NAME="E2:11"/><span class="kw">then </span>
<font color="Maroon" title="c1">u</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">u9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
;<br/>
<a NAME="E3:11"/><span class="kw">then </span><span class="lab"><font color="Green" title="E3">A1</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">u9</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v9</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">v</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">u9</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v9</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">x</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">v9</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">v</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">u9</font></span>)</span> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c6">x</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">u9</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c4">v9</font></span><br/>

<span class="kw">thus </span><a NAME="E5:11"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">u9</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c4">v9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:11"><span class="lab"><font color="Green" title="E3">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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