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<span class="kw">consider </span><font color="Maroon" title="c3">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E2:110_3_1"/><span class="lab"><font color="Green" title="E88">A4</font></span>: 
<font color="Maroon" title="c1">x</font> <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> <font color="Maroon" title="c3">r</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="surrealn.html#T62" target="_self" onmouseover="rs('surrealn/T62')" onmouseout="rh()">Th62</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">s</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E4:110_3_1"/><span class="lab"><font color="Green" title="E89">A5</font></span>: 
<font color="Maroon" title="c2">y</font> <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> <font color="Maroon" title="c4">s</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="surrealn.html#T62" target="_self" onmouseover="rs('surrealn/T62')" onmouseout="rh()">Th62</a></span>;<br/>
<a NAME="E5:110_3_1"/>
( <font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c2">y</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</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> <font color="Maroon" title="c3">r</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c2">y</font> &amp; <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> <font color="Maroon" title="c3">r</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c2">y</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</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> <font color="Maroon" title="c3">r</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> <font color="Maroon" title="c4">s</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:110_3_1"><span class="lab"><font color="Green" title="E88">A4</font></span></a>, <a class="txt" href="#E4:110_3_1"><span class="lab"><font color="Green" title="E89">A5</font></span></a>, <a class="ref" href="surrealr.html#T54" onmouseover="rs('surrealr/T54')" onmouseout="rh()">SURREALR:54</a></span>;<br/>
<a NAME="E6:110_3_1"/><span class="kw">then </span>
( <font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c2">y</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</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> <font color="Maroon" title="c3">r</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> <font color="Maroon" title="c4">s</font></span>)</span> &amp; <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> <font color="Maroon" title="c3">r</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> <font color="Maroon" title="c4">s</font></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> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">s</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surrealo.html#T4" onmouseover="rs('surrealo/T4')" onmouseout="rh()">SURREALO:4</a>, <a class="ref" href="surrealn.html#T57" target="_self" onmouseover="rs('surrealn/T57')" onmouseout="rh()">Th57</a></span>;<br/>
<a NAME="E7:110_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c2">y</font> <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"><font color="Maroon" title="c3">r</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">s</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surrealo.html#T4" onmouseover="rs('surrealo/T4')" onmouseout="rh()">SURREALO:4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:110_3_1"/>
<font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c2">y</font> is  <a href="surrealn.html#V2" title="SURREALN:attr.2">*real</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="surrealn.html#T62" target="_self" onmouseover="rs('surrealn/T62')" onmouseout="rh()">Th62</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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