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<span class="kw">let </span><font color="Maroon" title="c3">T</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cousin.html#K2" title="COUSIN:func.2">set_of_tagged_Division</a> <font color="Maroon" title="c2">D</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="c3">T</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/>

<span class="kw">consider </span><font color="Maroon" title="c4">s</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="valued_0.html#V7" title="VALUED_0:attr.7">non-decreasing</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <span class="kw"> such that </span><br/><a NAME="E2:56_1_1"/><span class="lab"><font color="Green" title="E39">A1</font></span>: 
<font color="Maroon" title="c3">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font>
 <span class="kw">and </span><br/><a NAME="E3:56_1_1"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">D</font>
 <span class="kw">and </span><br/><a NAME="E4:56_1_1"/>
 for <font color="Olive" title="b1">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">s</font> holds <br/><font color="Maroon" title="c4">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="integra1.html#K2" title="INTEGRA1:func.2">divset</a> (<font color="Maroon" title="c2">D</font>,<font color="Olive" title="b1">i</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cousin.html#D2" target="_self" onmouseover="rs('cousin/D2')" onmouseout="rh()">Def2</a></span>;<br/>
<span class="kw">thus </span><a NAME="E5:56_1_1"/>
 not <font color="Maroon" title="c3">T</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:56_1_1"><span class="lab"><font color="Green" title="E39">A1</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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