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<a NAME="E1:4_1_1"/>
 <a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <a href="rsspace.html#K6" title="RSSPACE:func.6">Zeroseq</a>  is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_1"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon" title="c1">rseq</font> =  <a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <a href="rsspace.html#K6" title="RSSPACE:func.6">Zeroseq</a>  as   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a> ;<br/>
<a NAME="E2:4_1_1_1"/>
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c1">rseq</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="rsspace.html#D6" title="RSSPACE:def.6">RSSPACE:def 6</a></i>;<br/>
<a NAME="E3:4_1_1_1"/><b>then </b>
<font color="Maroon" title="c1">rseq</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 
<b>by </b><i><a class="ref" href="seqm_3.html#D6" title="SEQM_3:def.6">SEQM_3:def 6</a></i>;<br/>
<b>hence </b><a NAME="E4:4_1_1_1"/>
 <a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <a href="rsspace.html#K6" title="RSSPACE:func.6">Zeroseq</a>  is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>
 <b>by </b><i><a class="ref" href="seqm_3.html#T73" title="SEQM_3:th.73">SEQM_3:73</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:4_1_1"/>
not  <a href="rsspace4.html#K1" title="RSSPACE4:func.1">the_set_of_BoundedRealSequences</a>  is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="ref" href="rsspace4.html#D1" target="_self" title="RSSPACE4:def.1">Def1</a></i>;<br/>


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