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<span class="kw">reconsider </span><font color="Maroon" title="c3">xx</font> = <font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c4">yy</font> = <font color="Maroon" title="c2">y</font> as   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:1"><span class="lab"><font color="Green" title="E1">A1</font></span></a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c5">a1</font>, <font color="Maroon" title="c6">a2</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">y1</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a>  st <font color="Olive" title="b1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> &amp; <font color="Olive" title="b2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> holds <br/><font color="Maroon" title="c5">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Olive" title="b2">y1</font> ) &amp; (  for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">y1</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a>  st <font color="Olive" title="b1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> &amp; <font color="Olive" title="b2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> holds <br/><font color="Maroon" title="c6">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Olive" title="b2">y1</font> ) implies <font color="Maroon" title="c5">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:1_1_2"/><span class="lab"><font color="Green" title="E2">A2</font></span>: 
 for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">y1</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a>  st <font color="Olive" title="b1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> &amp; <font color="Olive" title="b2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> holds <br/><font color="Maroon" title="c5">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Olive" title="b2">y1</font>
 <span class="kw">and </span><br/><a NAME="E3:1_1_2"/><span class="lab"><font color="Green" title="E3">A3</font></span>: 
 for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">y1</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a>  st <font color="Olive" title="b1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> &amp; <font color="Olive" title="b2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> holds <br/><font color="Maroon" title="c6">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x1</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Olive" title="b2">y1</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="c5">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a2</font></span><br/>

<a NAME="E4:1_1_2"/>
<font color="Maroon" title="c5">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">xx</font> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Maroon" title="c4">yy</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:1_1_2"><span class="lab"><font color="Green" title="E2">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:1_1_2"/>
<font color="Maroon" title="c5">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:1_1_2"><span class="lab"><font color="Green" title="E3">A3</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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