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<span class="kw">let </span><font color="Maroon" title="c1">seq</font> be   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</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">seq</font> is <a href="seq_2.html#V2" title="SEQ_2:attr.2">V99</a>() implies <span class="p1">(<span class="default"><a href="rinfsup1.html#K3" title="RINFSUP1:func.3">inferior_realsequence</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rinfsup1.html#K2" title="RINFSUP1:func.2">lower_bound</a> <font color="Maroon" title="c1">seq</font> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c2">Y1</font> = <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font></span>)</span> where <font color="Olive" title="b1">k</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> :  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> </span> } </span>  as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="rinfsup1.html#T29" target="_self" onmouseover="rs('rinfsup1/T29')" onmouseout="rh()">Th29</a></span>;<br/>
<span class="p1">(<span class="default"><a href="rinfsup1.html#K3" title="RINFSUP1:func.3">inferior_realsequence</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> = 
 <a href="seq_4.html#K3" title="SEQ_4:func.3">lower_bound</a> <font color="Maroon" title="c2">Y1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rinfsup1.html#D4" target="_self" onmouseover="rs('rinfsup1/D4')" onmouseout="rh()">Def4</a></span>
<br/>.= 
 <a href="rinfsup1.html#K2" title="RINFSUP1:func.2">lower_bound</a> <font color="Maroon" title="c1">seq</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="setlim_1.html#T5" onmouseover="rs('setlim_1/T5')" onmouseout="rh()">SETLIM_1:5</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:38"/>
( <font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V2" title="SEQ_2:attr.2">V99</a>() implies <span class="p1">(<span class="default"><a href="rinfsup1.html#K3" title="RINFSUP1:func.3">inferior_realsequence</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rinfsup1.html#K2" title="RINFSUP1:func.2">lower_bound</a> <font color="Maroon" title="c1">seq</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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