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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="hidden.html#M2" title="HIDDEN:mode.2">set</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><br/>  for <font color="Olive" title="b2">f</font> being   <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="Olive" title="b1">Y</font> holds   <a href="rsspace4.html#K6" title="RSSPACE4:func.6">modetrans</a> (<font color="Olive" title="b2">f</font>,<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">Y</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">f</font></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">  for <font color="Olive" title="b1">f</font> being   <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> holds   <a href="rsspace4.html#K6" title="RSSPACE4:func.6">modetrans</a> (<font color="Olive" title="b1">f</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">f</font></span><br/><span class="kw">let </span><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>; <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="rsspace4.html#K6" title="RSSPACE4:func.6">modetrans</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">f</font></span><br/>





<a NAME="E1:32"/>
<font color="Maroon" title="c3">f</font> <a href="tarski.html#R2" title="TARSKI: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>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rsspace4.html#D5" target="_self" onmouseover="rs('rsspace4/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:32"/>
 <a href="rsspace4.html#K6" title="RSSPACE4:func.6">modetrans</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rsspace4.html#D7" target="_self" onmouseover="rs('rsspace4/D7')" onmouseout="rh()">Def7</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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