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<span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font> be   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c4">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c3">b</font> <a href="xreal_0.html#K1" title="XREAL_0:func.1">-'</a> <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">b</font> <a href="xreal_0.html#K1" title="XREAL_0:func.1">-'</a> <font color="Maroon" title="c4">c</font> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:221"/><span class="lab"><font color="Green" title="E72">A1</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">b</font>
 <span class="kw">and </span><br/><a NAME="E2:221"/><span class="lab"><font color="Green" title="E73">A2</font></span>: 
<font color="Maroon" title="c4">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">b</font> <a href="xreal_0.html#K1" title="XREAL_0:func.1">-'</a> <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">b</font> <a href="xreal_0.html#K1" title="XREAL_0:func.1">-'</a> <font color="Maroon" title="c4">c</font></span><br/>

<a NAME="E3:221"/><span class="lab"><font color="Green" title="E74">A3</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:221"><span class="lab"><font color="Green" title="E73">A2</font></span></a>, <a class="ref" href="xreal_1.html#T15" target="_self" title="XREAL_1:th.15">Th17</a></span>;<br/>
<a NAME="E4:221"/>
<font color="Maroon" title="c3">b</font> <a href="xreal_0.html#K1" title="XREAL_0:func.1">-'</a> <font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:221"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="txt" href="#E2:221"><span class="lab"><font color="Green" title="E73">A2</font></span></a>, <a class="ref" href="xreal_1.html#T233" target="_self" title="XREAL_1:th.233">Th235</a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:221"/>
<font color="Maroon" title="c3">b</font> <a href="xreal_0.html#K1" title="XREAL_0:func.1">-'</a> <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">b</font> <a href="xreal_0.html#K1" title="XREAL_0:func.1">-'</a> <font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:221"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="txt" href="#E3:221"><span class="lab"><font color="Green" title="E74">A3</font></span></a>, <a class="ref" href="xreal_1.html#T233" target="_self" title="XREAL_1:th.233">Th235</a></span>; <a class="txt" 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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