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<span class="kw">thus </span><a NAME="E1:50_1_1"/>
( <font color="Maroon" title="c1">x</font> is  <a href="surreali.html#V2" title="SURREALI:attr.2">positive</a>  implies  ex <font color="Olive" title="b1">IT</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a> st <font color="Olive" title="b1">IT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surreali.html#K10" title="SURREALI:func.10">inv</a> <font color="Maroon" title="c1">x</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"> (  not <font color="Maroon" title="c1">x</font> is  <a href="surreali.html#V2" title="SURREALI:attr.2">positive</a>  implies  ex <font color="Olive">b<sub>1</sub></font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a> st  <a href="surrealr.html#K2" title="SURREALR:func.2">-</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surreali.html#K10" title="SURREALI:func.10">inv</a> <span class="p1">(<span class="default"><a href="surrealr.html#K2" title="SURREALR:func.2">-</a> <font color="Maroon" title="c1">x</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E2:50_1_1"/>
 not <font color="Maroon" title="c1">x</font> is  <a href="surreali.html#V2" title="SURREALI:attr.2">positive</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">  ex <font color="Olive">b<sub>1</sub></font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a> st  <a href="surrealr.html#K2" title="SURREALR:func.2">-</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surreali.html#K10" title="SURREALI:func.10">inv</a> <span class="p1">(<span class="default"><a href="surrealr.html#K2" title="SURREALR:func.2">-</a> <font color="Maroon" title="c1">x</font></span>)</span></span><br/>

<a NAME="E3:50_1_1"/><span class="kw">then </span>
 <a href="surrealr.html#K2" title="SURREALR:func.2">-</a> <font color="Maroon" title="c1">x</font> is  <a href="surreali.html#V2" title="SURREALI:attr.2">positive</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E41">A1</font></span></a>, <a class="ref" href="surrealr.html#T10" onmouseover="rs('surrealr/T10')" onmouseout="rh()">SURREALR:10</a>, <a class="ref" href="surrealr.html#T23" onmouseover="rs('surrealr/T23')" onmouseout="rh()">SURREALR:23</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c2">i</font> =  <a href="surreali.html#K10" title="SURREALI:func.10">inv</a> <span class="p1">(<span class="default"><a href="surrealr.html#K2" title="SURREALR:func.2">-</a> <font color="Maroon" title="c1">x</font></span>)</span> as   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a> ;<br/>
<a NAME="E5:50_1_1"/>
 <a href="surrealr.html#K2" title="SURREALR:func.2">-</a> <span class="p1">(<span class="default"><a href="surrealr.html#K2" title="SURREALR:func.2">-</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">i</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E6:50_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a> st  <a href="surrealr.html#K2" title="SURREALR:func.2">-</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surreali.html#K10" title="SURREALI:func.10">inv</a> <span class="p1">(<span class="default"><a href="surrealr.html#K2" title="SURREALR:func.2">-</a> <font color="Maroon" title="c1">x</font></span>)</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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