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<span class="kw">let </span><font color="Maroon" title="c2">I1</font>, <font color="Maroon" title="c3">I2</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"> ( ( <font color="Maroon" title="c1">x</font> is  <a href="surreali.html#V2" title="SURREALI:attr.2">positive</a>  &amp; <font color="Maroon" title="c2">I1</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> &amp; <font color="Maroon" title="c3">I2</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> implies <font color="Maroon" title="c2">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">I2</font> ) &amp; (  not <font color="Maroon" title="c1">x</font> is  <a href="surreali.html#V2" title="SURREALI:attr.2">positive</a>  &amp;  <a href="surrealr.html#K2" title="SURREALR:func.2">-</a> <font color="Maroon" title="c2">I1</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> &amp;  <a href="surrealr.html#K2" title="SURREALR:func.2">-</a> <font color="Maroon" title="c3">I2</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> implies <font color="Maroon" title="c2">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">I2</font> ) )</span><br/>

<a NAME="E1:50_1_2"/>
( <font color="Maroon" title="c2">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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">I1</font></span>)</span> &amp; <font color="Maroon" title="c3">I2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c3">I2</font></span>)</span> )
 
;<br/>
<span class="kw">hence </span><a NAME="E2:50_1_2"/>
( ( <font color="Maroon" title="c1">x</font> is  <a href="surreali.html#V2" title="SURREALI:attr.2">positive</a>  &amp; <font color="Maroon" title="c2">I1</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> &amp; <font color="Maroon" title="c3">I2</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> implies <font color="Maroon" title="c2">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">I2</font> ) &amp; (  not <font color="Maroon" title="c1">x</font> is  <a href="surreali.html#V2" title="SURREALI:attr.2">positive</a>  &amp;  <a href="surrealr.html#K2" title="SURREALR:func.2">-</a> <font color="Maroon" title="c2">I1</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> &amp;  <a href="surrealr.html#K2" title="SURREALR:func.2">-</a> <font color="Maroon" title="c3">I2</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> implies <font color="Maroon" title="c2">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">I2</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"> verum</span><br/>


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