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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</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">f</font> being <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> <a href="pscomp_1.html#NM1" title="PSCOMP_1:NM.1">RealMap</a> of <font color="Maroon" title="c1">T</font> holds   <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">inf</a> <font color="Olive" title="b1">f</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">sup</a> <font color="Olive" title="b1">f</font></span><br/><b>let </b><font color="Maroon" title="c2">f</font> be  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> <a href="pscomp_1.html#NM1" title="PSCOMP_1:NM.1">RealMap</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">inf</a> <font color="Maroon" title="c2">f</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">sup</a> <font color="Maroon" title="c2">f</font></span><br/>



<a NAME="E1:81"/>
( <font color="Maroon" title="c2">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> is <a href="seq_4.html#V2" title="SEQ_4:attr.2">bounded_below</a> &amp; <font color="Maroon" title="c2">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> is <a href="seq_4.html#V1" title="SEQ_4:attr.1">bounded_above</a> )
 
<b>by </b><i><a class="ref" href="pscomp_1.html#D11" target="_self" title="PSCOMP_1:def.11">Def11</a>, <a class="ref" href="pscomp_1.html#D12" target="_self" title="PSCOMP_1:def.12">Def12</a></i>;<br/>
<a NAME="E2:81"/><b>then </b>
<font color="Maroon" title="c2">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> is <a href="seq_4.html#V3" title="SEQ_4:attr.3">bounded</a>
 
<b>by </b><i><a class="ref" href="seq_4.html#D3" title="SEQ_4:def.3">SEQ_4:def 3</a></i>;<br/>
<b>hence </b><a NAME="E3:81"/>
 <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">inf</a> <font color="Maroon" title="c2">f</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">sup</a> <font color="Maroon" title="c2">f</font>
 <b>by </b><i><a class="ref" href="seq_4.html#T24" title="SEQ_4:th.24">SEQ_4:24</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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