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<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</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">  for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x1R</font>, <font color="Olive" title="b3">y1</font>, <font color="Olive" title="b4">y1R</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a>  st  <a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a>  <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Olive" title="b1">x1</font> &amp; <font color="Olive" title="b1">x1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Olive" title="b2">x1R</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a>  <a href="surrealo.html#K1" title="SURREALO:func.1">1_No</a>  &amp;  <a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a>  <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Olive" title="b3">y1</font> &amp; <font color="Olive" title="b3">y1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Olive" title="b4">y1R</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a>  <a href="surrealo.html#K1" title="SURREALO:func.1">1_No</a>  &amp; <font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Olive" title="b3">y1</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Olive" title="b1">x1</font> holds <br/><font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Olive" title="b2">x1R</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Olive" title="b4">y1R</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">x1</font>, <font color="Maroon" title="c4">x1R</font>, <font color="Maroon" title="c5">y1</font>, <font color="Maroon" title="c6">y1R</font> be   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</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"> (  <a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a>  <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Maroon" title="c3">x1</font> &amp; <font color="Maroon" title="c3">x1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a>  <a href="surrealo.html#K1" title="SURREALO:func.1">1_No</a>  &amp;  <a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a>  <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Maroon" title="c5">y1</font> &amp; <font color="Maroon" title="c5">y1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a>  <a href="surrealo.html#K1" title="SURREALO:func.1">1_No</a>  &amp; <font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c5">y1</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c3">x1</font> implies <font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:45"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
(  <a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a>  <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Maroon" title="c3">x1</font> &amp; <font color="Maroon" title="c3">x1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a>  <a href="surrealo.html#K1" title="SURREALO:func.1">1_No</a>  &amp;  <a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a>  <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Maroon" title="c5">y1</font> &amp; <font color="Maroon" title="c5">y1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a>  <a href="surrealo.html#K1" title="SURREALO:func.1">1_No</a>  &amp; <font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c5">y1</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c3">x1</font> )
 ; <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> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font></span><br/>

<a NAME="E2:45"/><span class="lab"><font color="Green" title="E39">A2</font></span>: 
(  <a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a>  <a href="surrealo.html#R1" title="SURREALO:pred.1">&lt;=</a> <font color="Maroon" title="c3">x1</font> &amp;  <a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a>  <a href="surrealo.html#R1" title="SURREALO:pred.1">&lt;=</a> <font color="Maroon" title="c5">y1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E38">A1</font></span></a></span>;<br/>
<a NAME="E3:45"/>
 <a href="surrealo.html#K1" title="SURREALO:func.1">1_No</a>  is  <a href="surreali.html#V2" title="SURREALI:attr.2">positive</a> 
 
;<br/>
<a NAME="E4:45"/><span class="kw">then </span>
(  <a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a>  <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Maroon" title="c3">x1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font> &amp;  <a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a>  <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Maroon" title="c5">y1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="ref" href="surrealo.html#T4" onmouseover="rs('surrealo/T4')" onmouseout="rh()">SURREALO:4</a></span>;<br/>
<a NAME="E5:45"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A3</font></span>: 
(  <a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a>  <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Maroon" title="c4">x1R</font> &amp;  <a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a>  <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Maroon" title="c6">y1R</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:45"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="surrealr.html#T72" onmouseover="rs('surrealr/T72')" onmouseout="rh()">SURREALR:72</a></span>;<br/>
<a NAME="E6:45"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c5">y1</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c3">x1</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="ref" href="surrealr.html#T70" onmouseover="rs('surrealr/T70')" onmouseout="rh()">SURREALR:70</a></span>;<br/>
<a NAME="E7:45"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A4</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c5">y1</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c3">x1</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:45"><span class="lab"><font color="Green" title="E40">A3</font></span></a>, <a class="ref" href="surrealr.html#T70" onmouseover="rs('surrealr/T70')" onmouseout="rh()">SURREALR:70</a></span>;<br/>
<a NAME="E8:45"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c5">y1</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a> <font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font></span>)</span> &amp; <font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font></span>)</span> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a> <font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <a href="surrealo.html#K1" title="SURREALO:func.1">1_No</a> &amp; <font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <a href="surrealo.html#K1" title="SURREALO:func.1">1_No</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surrealr.html#T51" onmouseover="rs('surrealr/T51')" onmouseout="rh()">SURREALR:51</a>, <a class="ref" href="surrealr.html#T69" onmouseover="rs('surrealr/T69')" onmouseout="rh()">SURREALR:69</a>, <a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E38">A1</font></span></a></span>;<br/>
<a NAME="E9:45"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c5">y1</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a> <font color="Maroon" title="c1">x</font>
 
<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/>
<a NAME="E10:45"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A5</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c5">y1</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a> <font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surrealr.html#T51" onmouseover="rs('surrealr/T51')" onmouseout="rh()">SURREALR:51</a></span>;<br/>
<a NAME="E11:45"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c3">x1</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font></span>)</span></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font></span>)</span></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a> <font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surrealr.html#T51" onmouseover="rs('surrealr/T51')" onmouseout="rh()">SURREALR:51</a>, <a class="ref" href="surrealr.html#T69" onmouseover="rs('surrealr/T69')" onmouseout="rh()">SURREALR:69</a></span>;<br/>
<a NAME="E12:45"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c3">x1</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a> <font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font></span>)</span> &amp; <font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font></span>)</span> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a> <font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">y1R</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font></span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surrealr.html#T69" onmouseover="rs('surrealr/T69')" onmouseout="rh()">SURREALR:69</a>, <a class="ref" href="surrealo.html#T4" onmouseover="rs('surrealo/T4')" onmouseout="rh()">SURREALO:4</a>, <a class="ref" href="surrealr.html#T51" onmouseover="rs('surrealr/T51')" onmouseout="rh()">SURREALR:51</a></span>;<br/>
<a NAME="E13:45"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A6</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c3">x1</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a> <font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">y1R</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font></span>)</span></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/>
<a NAME="E14:45"/>
( <font color="Maroon" title="c6">y1R</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font></span>)</span> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a> <font color="Maroon" title="c6">y1R</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <a href="surrealo.html#K1" title="SURREALO:func.1">1_No</a> &amp; <font color="Maroon" title="c6">y1R</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <a href="surrealo.html#K1" title="SURREALO:func.1">1_No</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y1R</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surrealr.html#T51" onmouseover="rs('surrealr/T51')" onmouseout="rh()">SURREALR:51</a>, <a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E38">A1</font></span></a></span>;<br/>
<a NAME="E15:45"/><span class="kw">then </span>
<font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">y1R</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font></span>)</span></span>)</span> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a> <font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surrealr.html#T51" onmouseover="rs('surrealr/T51')" onmouseout="rh()">SURREALR:51</a></span>;<br/>
<a NAME="E16:45"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c3">x1</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a> <font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:45"><span class="lab"><font color="Green" title="E43">A6</font></span></a>, <a class="ref" href="surrealo.html#T4" onmouseover="rs('surrealo/T4')" onmouseout="rh()">SURREALO:4</a></span>;<br/>
<a NAME="E17:45"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c5">y1</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:45"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <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="E18:45"/>
<font color="Maroon" title="c1">x</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">x1R</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Maroon" title="c2">y</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c6">y1R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:45"><span class="lab"><font color="Green" title="E42">A5</font></span></a>, <a class="ref" href="surrealo.html#T4" onmouseover="rs('surrealo/T4')" onmouseout="rh()">SURREALO:4</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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