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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">Y</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon" title="c3">f</font> be  <a href="rsspace4.html#V1" title="RSSPACE4:attr.1">bounded</a> <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font>;<br/>





<a NAME="E1:36"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rsspace4.html#K4" title="RSSPACE4:func.4">BoundedFunctions</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>
 
<b>by </b><i><a class="ref" href="rsspace4.html#D5" target="_self" title="RSSPACE4:def.5">Def5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">f'</font> = <font color="Maroon" title="c3">f</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="rsspace4.html#K8" title="RSSPACE4:func.8">BoundedFunctionsNorm</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">f</font> = 
 <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">sup</a> <span class="p1">(<span class="default"><a href="rsspace4.html#K7" title="RSSPACE4:func.7">PreNorms</a> <span class="p2">(<span class="default"><a href="rsspace4.html#K6" title="RSSPACE4:func.6">modetrans</a> <font color="Maroon" title="c4">f'</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="rsspace4.html#E1:36"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="rsspace4.html#D9" target="_self" title="RSSPACE4:def.9">Def9</a></i>
<br/>.= 
 <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">sup</a> <span class="p1">(<span class="default"><a href="rsspace4.html#K7" title="RSSPACE4:func.7">PreNorms</a> <font color="Maroon" title="c3">f</font></span>)</span>
<b>by </b><i><a class="ref" href="rsspace4.html#T16" target="_self" title="RSSPACE4:th.16">Th16</a></i>
;<br/>


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