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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">seq</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c3">k</font>, <font color="Maroon" title="c4">m</font> be    <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> ;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">n</font> be    <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> ;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="lopban_3.html#K2" title="LOPBAN_3:func.2">^\</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="lopban_3.html#K2" title="LOPBAN_3:func.2">^\</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c5">n</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="lopban_3.html#K2" title="LOPBAN_3:func.2">^\</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c4">m</font></span>)</span>
<b>by </b><i><a class="ref" href="lopban_3.html#D6" target="_self" title="LOPBAN_3:def.6">Def6</a></i>
<br/>.= 
<font color="Maroon" title="c2">seq</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span>
<b>by </b><i><a class="ref" href="lopban_3.html#D6" target="_self" title="LOPBAN_3:def.6">Def6</a></i>
<br/>.= 
<font color="Maroon" title="c2">seq</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c4">m</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="lopban_3.html#K2" title="LOPBAN_3:func.2">^\</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span>
<b>by </b><i><a class="ref" href="lopban_3.html#D6" target="_self" title="LOPBAN_3:def.6">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="lopban_3.html#K2" title="LOPBAN_3:func.2">^\</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="lopban_3.html#K2" title="LOPBAN_3:func.2">^\</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c5">n</font>
<b>by </b><i><a class="ref" href="lopban_3.html#D6" target="_self" title="LOPBAN_3:def.6">Def6</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:18"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="lopban_3.html#K2" title="LOPBAN_3:func.2">^\</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="lopban_3.html#K2" title="LOPBAN_3:func.2">^\</a> <font color="Maroon" title="c4">m</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="lopban_3.html#K2" title="LOPBAN_3:func.2">^\</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="lopban_3.html#K2" title="LOPBAN_3:func.2">^\</a> <font color="Maroon" title="c3">k</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


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