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<b>let </b><font color="Maroon" title="c1">seq</font> be   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>;<br/>

<b>assume </b><a NAME="E1:17"/>
<font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a>
 ;<br/>

<a NAME="E2:17"/><b>then </b>
( not  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c1">seq</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c1">seq</font> is <a href="seq_4.html#V2" title="SEQ_4:attr.2">bounded_below</a> )
 
<b>by </b><i><a class="ref" href="rinfsup1.html#T6" target="_self" title="RINFSUP1:th.6">Th6</a>, <a class="ref" href="setlim_1.html#T8" title="SETLIM_1:th.8">SETLIM_1:8</a></i>;<br/>
<b>then </b> <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">inf</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c1">seq</font></span>)</span> = 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">sup</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K4" title="PSCOMP_1:func.4">-</a> <span class="p3">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c1">seq</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="pscomp_1.html#T17" title="PSCOMP_1:th.17">PSCOMP_1:17</a></i>
<br/>.= 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">sup</a> <span class="p2">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p3">(<span class="default"><a href="partfun3.html#K6" title="PARTFUN3:func.6">-</a> <font color="Maroon" title="c1">seq</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rinfsup1.html#T4" target="_self" title="RINFSUP1:th.4">Th4</a></i>
;<br/>
<b>hence </b><a NAME="E4:17"/>
 <a href="rinfsup1.html#K2" title="RINFSUP1:func.2">inf</a> <font color="Maroon" title="c1">seq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="rinfsup1.html#K1" title="RINFSUP1:func.1">sup</a> <span class="p2">(<span class="default"><a href="partfun3.html#K6" title="PARTFUN3:func.6">-</a> <font color="Maroon" title="c1">seq</font></span>)</span></span>)</span>
 ;<br/>


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