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<b>let </b><font color="Maroon" title="c1">E</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">C</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K10" title="AFINSQ_1:func.10">^omega</a> </span>)</span><br/> for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K10" title="AFINSQ_1:func.10">^omega</a>   st <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">C</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a>  &amp; <font color="Olive" title="b3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">C</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a>  holds <br/><font color="Olive" title="b2">a</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Olive" title="b3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">C</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a> </span><br/><b>let </b><font color="Maroon" title="c2">C</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K10" title="AFINSQ_1:func.10">^omega</a> </span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K10" title="AFINSQ_1:func.10">^omega</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a>  &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a>  holds <br/><font color="Olive" title="b1">a</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a> </span><br/><b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K10" title="AFINSQ_1:func.10">^omega</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a>  &amp; <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a>  implies <font color="Maroon" title="c3">a</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a>  )</span><br/>







<b>assume </b><a NAME="E1:68"/><i><font color="Green" title="E50">A1</font></i>: 
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a>  &amp; <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a> </span><br/>

<b>then consider </b><font color="Maroon" title="c5">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E3:68"/><i><font color="Green" title="E51">A2</font></i>: 
( <font color="Maroon" title="c5">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c5">k</font> )
 <b>by </b><i><a class="ref" href="flang_3.html#T48" target="_self" title="FLANG_3:th.48">Th48</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">l</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E5:68"/><i><font color="Green" title="E52">A3</font></i>: 
( <font color="Maroon" title="c6">l</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c6">l</font> )
 <b>by </b><i><a class="txt" href="#E1:68"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="flang_3.html#T48" target="_self" title="FLANG_3:th.48">Th48</a></i>;<br/>
<a NAME="E6:68"/><i><font color="Green" title="E53">A4</font></i>: 
<font color="Maroon" title="c5">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">l</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="#E3:68"><i><font color="Green" title="E51">A2</font></i></a></i>;<br/>
<a NAME="E7:68"/>
<font color="Maroon" title="c3">a</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">l</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E3:68"><i><font color="Green" title="E51">A2</font></i></a>, <a class="txt" href="#E5:68"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="flang_1.html#T41" title="FLANG_1:th.41">FLANG_1:41</a></i>;<br/>
<b>hence </b><a NAME="E8:68"/>
<font color="Maroon" title="c3">a</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a> 
 <b>by </b><i><a class="txt" href="#E6:68"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="flang_3.html#T48" target="_self" title="FLANG_3:th.48">Th48</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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