<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">T</font> be   <a href="c0sp3.html#NM1" title="C0SP3:NM.1">NormedLinearTopSpace</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">  for <font color="Olive" title="b1">RNS</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>  st <font color="Maroon" title="c1">T</font> is  <a href="rlvect_5.html#V1" title="RLVECT_5:attr.1">finite-dimensional</a>  &amp; <font color="Olive" title="b1">RNS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normsp_1.html#G1" title="NORMSP_1:aggr.1">NORMSTR</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c1">T</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">T</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c1">T</font>, the <a href="normsp_0.html#U1" title="NORMSP_0:sel.1">normF</a> of <font color="Maroon" title="c1">T</font> #) holds <br/>( <font color="Olive" title="b1">RNS</font> is  <a href="rlvect_5.html#V1" title="RLVECT_5:attr.1">finite-dimensional</a>  &amp;  <a href="rlvect_5.html#K1" title="RLVECT_5:func.1">dim</a> <font color="Olive" title="b1">RNS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_5.html#K1" title="RLVECT_5:func.1">dim</a> <font color="Maroon" title="c1">T</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">RNS</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</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">T</font> is  <a href="rlvect_5.html#V1" title="RLVECT_5:attr.1">finite-dimensional</a>  &amp; <font color="Maroon" title="c2">RNS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normsp_1.html#G1" title="NORMSP_1:aggr.1">NORMSTR</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c1">T</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">T</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c1">T</font>, the <a href="normsp_0.html#U1" title="NORMSP_0:sel.1">normF</a> of <font color="Maroon" title="c1">T</font> #) implies ( <font color="Maroon" title="c2">RNS</font> is  <a href="rlvect_5.html#V1" title="RLVECT_5:attr.1">finite-dimensional</a>  &amp;  <a href="rlvect_5.html#K1" title="RLVECT_5:func.1">dim</a> <font color="Maroon" title="c2">RNS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_5.html#K1" title="RLVECT_5:func.1">dim</a> <font color="Maroon" title="c1">T</font> ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:16"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
( <font color="Maroon" title="c1">T</font> is  <a href="rlvect_5.html#V1" title="RLVECT_5:attr.1">finite-dimensional</a>  &amp; <font color="Maroon" title="c2">RNS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normsp_1.html#G1" title="NORMSP_1:aggr.1">NORMSTR</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c1">T</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">T</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c1">T</font>, the <a href="normsp_0.html#U1" title="NORMSP_0:sel.1">normF</a> of <font color="Maroon" title="c1">T</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"> ( <font color="Maroon" title="c2">RNS</font> is  <a href="rlvect_5.html#V1" title="RLVECT_5:attr.1">finite-dimensional</a>  &amp;  <a href="rlvect_5.html#K1" title="RLVECT_5:func.1">dim</a> <font color="Maroon" title="c2">RNS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_5.html#K1" title="RLVECT_5:func.1">dim</a> <font color="Maroon" title="c1">T</font> )</span><br/>

<a NAME="E2:16"/><span class="kw">then </span>
 <a href="rlvect_1.html#G1" title="RLVECT_1:aggr.1">RLSStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c1">T</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">T</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c1">T</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#G1" title="RLVECT_1:aggr.1">RLSStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">RNS</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c2">RNS</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c2">RNS</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c2">RNS</font> #)
 
;<br/>
<span class="kw">hence </span><a NAME="E3:16"/>
( <font color="Maroon" title="c2">RNS</font> is  <a href="rlvect_5.html#V1" title="RLVECT_5:attr.1">finite-dimensional</a>  &amp;  <a href="rlvect_5.html#K1" title="RLVECT_5:func.1">dim</a> <font color="Maroon" title="c2">RNS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_5.html#K1" title="RLVECT_5:func.1">dim</a> <font color="Maroon" title="c1">T</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="neurons1.html#T21" target="_self" onmouseover="rs('neurons1/T21')" onmouseout="rh()">Th21</a>, <a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E13">A1</font></span></a></span>; <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/>


</div>
