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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="measure5.html#V2" title="MEASURE5:attr.2">closed_interval</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</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">Y</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a> holds   <a href="ordeq_01.html#K5" title="ORDEQ_01:func.5">R_NormSpace_of_ContinuousFunctions</a> (<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">Y</font>) is   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a></span><br/><span class="kw">let </span><font color="Maroon" title="c2">Y</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">  <a href="ordeq_01.html#K5" title="ORDEQ_01:func.5">R_NormSpace_of_ContinuousFunctions</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>) is   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a></span><br/>



<a NAME="E1:33"/>
 <a href="rlvect_1.html#G1" title="RLVECT_1:aggr.1">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="ordeq_01.html#K1" title="ORDEQ_01:func.1">ContinuousFunctions</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="rsspace.html#K7" title="RSSPACE:func.7">Zero_</a> (<span class="p2">(<span class="default"><a href="ordeq_01.html#K1" title="ORDEQ_01:func.1">ContinuousFunctions</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="rsspace4.html#K5" title="RSSPACE4:func.5">R_VectorSpace_of_BoundedFunctions</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)</span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="rsspace.html#K5" title="RSSPACE:func.5">Add_</a> (<span class="p2">(<span class="default"><a href="ordeq_01.html#K1" title="ORDEQ_01:func.1">ContinuousFunctions</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="rsspace4.html#K5" title="RSSPACE4:func.5">R_VectorSpace_of_BoundedFunctions</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)</span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="rsspace.html#K6" title="RSSPACE:func.6">Mult_</a> (<span class="p2">(<span class="default"><a href="ordeq_01.html#K1" title="ORDEQ_01:func.1">ContinuousFunctions</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="rsspace4.html#K5" title="RSSPACE4:func.5">R_VectorSpace_of_BoundedFunctions</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)</span>)</span>)</span>)</span> #) is   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rsspace.html#T11" onmouseover="rs('rsspace/T11')" onmouseout="rh()">RSSPACE:11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:33"/>
 <a href="ordeq_01.html#K5" title="ORDEQ_01:func.5">R_NormSpace_of_ContinuousFunctions</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>) is   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="ordeq_01.html#E27"><span class="lab"><font color="Green" title="E16">Lm3</font></span></a>, <a class="ref" href="rsspace3.html#T2" onmouseover="rs('rsspace3/T2')" onmouseout="rh()">RSSPACE3:2</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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