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<span class="kw">let </span><font color="Maroon" title="c1">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">RNS</font> is  <a href="rlvect_5.html#V1" title="RLVECT_5:attr.1">finite-dimensional</a>  implies  ex <font color="Olive" title="b1">T</font> being   <a href="c0sp3.html#NM1" title="C0SP3:NM.1">NormedLinearTopSpace</a> st <br/>(  <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">RNS</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c1">RNS</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">RNS</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c1">RNS</font>, the <a href="normsp_0.html#U1" title="NORMSP_0:sel.1">normF</a> of <font color="Maroon" title="c1">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="Olive" title="b1">T</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Olive" title="b1">T</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Olive" title="b1">T</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Olive" title="b1">T</font>, the <a href="normsp_0.html#U1" title="NORMSP_0:sel.1">normF</a> of <font color="Olive" title="b1">T</font> #) &amp; <font color="Olive" title="b1">T</font> is  <a href="rlvect_5.html#V1" title="RLVECT_5:attr.1">finite-dimensional</a>  ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:15"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
<font color="Maroon" title="c1">RNS</font> is  <a href="rlvect_5.html#V1" title="RLVECT_5:attr.1">finite-dimensional</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">  ex <font color="Olive" title="b1">T</font> being   <a href="c0sp3.html#NM1" title="C0SP3:NM.1">NormedLinearTopSpace</a> st <br/>(  <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">RNS</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c1">RNS</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">RNS</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c1">RNS</font>, the <a href="normsp_0.html#U1" title="NORMSP_0:sel.1">normF</a> of <font color="Maroon" title="c1">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="Olive" title="b1">T</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Olive" title="b1">T</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Olive" title="b1">T</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Olive" title="b1">T</font>, the <a href="normsp_0.html#U1" title="NORMSP_0:sel.1">normF</a> of <font color="Olive" title="b1">T</font> #) &amp; <font color="Olive" title="b1">T</font> is  <a href="rlvect_5.html#V1" title="RLVECT_5:attr.1">finite-dimensional</a>  )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c2">T</font> being   <a href="c0sp3.html#NM1" title="C0SP3:NM.1">NormedLinearTopSpace</a><span class="kw"> such that </span><br/><a NAME="E3:15"/><span class="lab"><font color="Green" title="E13">A2</font></span>: 
 <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">RNS</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c1">RNS</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">RNS</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c1">RNS</font>, the <a href="normsp_0.html#U1" title="NORMSP_0:sel.1">normF</a> of <font color="Maroon" title="c1">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="c2">T</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c2">T</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c2">T</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c2">T</font>, the <a href="normsp_0.html#U1" title="NORMSP_0:sel.1">normF</a> of <font color="Maroon" title="c2">T</font> #)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="neurons1.html#T23" target="_self" onmouseover="rs('neurons1/T23')" onmouseout="rh()">Th23</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c2">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"> (  <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">RNS</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c1">RNS</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">RNS</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c1">RNS</font>, the <a href="normsp_0.html#U1" title="NORMSP_0:sel.1">normF</a> of <font color="Maroon" title="c1">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="c2">T</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c2">T</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c2">T</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c2">T</font>, the <a href="normsp_0.html#U1" title="NORMSP_0:sel.1">normF</a> of <font color="Maroon" title="c2">T</font> #) &amp; <font color="Maroon" title="c2">T</font> is  <a href="rlvect_5.html#V1" title="RLVECT_5:attr.1">finite-dimensional</a>  )</span><br/>

<a NAME="E4:15"/>
 <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">T</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c2">T</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c2">T</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c2">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="c1">RNS</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c1">RNS</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">RNS</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c1">RNS</font> #)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:15"><span class="lab"><font color="Green" title="E13">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:15"/>
(  <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">RNS</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c1">RNS</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">RNS</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c1">RNS</font>, the <a href="normsp_0.html#U1" title="NORMSP_0:sel.1">normF</a> of <font color="Maroon" title="c1">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="c2">T</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c2">T</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c2">T</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c2">T</font>, the <a href="normsp_0.html#U1" title="NORMSP_0:sel.1">normF</a> of <font color="Maroon" title="c2">T</font> #) &amp; <font color="Maroon" title="c2">T</font> is  <a href="rlvect_5.html#V1" title="RLVECT_5:attr.1">finite-dimensional</a>  )
 <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="#E1:15"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E3:15"><span class="lab"><font color="Green" title="E13">A2</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/>


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