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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">f</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="lopban_1.html#K10" title="LOPBAN_1:func.10">BoundedLinearOperators</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font>;<br/>



<a NAME="E1:14"/>
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> is  <a href="lopban_1.html#V3" title="LOPBAN_1:attr.3">bounded</a> <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="lopban_2.html#T3" target="_self" title="LOPBAN_2:th.3">Th3</a></i>;<br/>
<a NAME="E2:14"/><b>then </b>
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="lopban_1.html#K10" title="LOPBAN_1:func.10">BoundedLinearOperators</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="lopban_1.html#D10" title="LOPBAN_1:def.10">LOPBAN_1:def 10</a></i>;<br/>
<a NAME="E3:14"/><b>then </b><i><font color="Green" title="E10">A1</font></i>: 
 <a href="lopban_1.html#K13" title="LOPBAN_1:func.13">modetrans</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font></span>)</span>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="lopban_1.html#D12" title="LOPBAN_1:def.12">LOPBAN_1:def 12</a></i>;<br/>
<b>hence </b><font color="Maroon" title="c2">f</font> <a href="lopban_2.html#K3" title="LOPBAN_2:func.3">*</a> <span class="p1">(<span class="default"><a href="lopban_2.html#K6" title="LOPBAN_2:func.6">FuncUnit</a> <font color="Maroon" title="c1">X</font></span>)</span> = 
 <a href="lopban_1.html#K13" title="LOPBAN_1:func.13">modetrans</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font>
<b>by </b><i><a class="ref" href="lopban_2.html#T6" target="_self" title="LOPBAN_2:th.6">Th6</a></i>
<br/>.= 
<font color="Maroon" title="c2">f</font>
<b>by </b><i><a class="ref" href="lopban_1.html#D12" title="LOPBAN_1:def.12">LOPBAN_1:def 12</a></i>
;<br/><br/>

<b>thus </b><span class="p1">(<span class="default"><a href="lopban_2.html#K6" title="LOPBAN_2:func.6">FuncUnit</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="lopban_2.html#K3" title="LOPBAN_2:func.3">*</a> <font color="Maroon" title="c2">f</font> = 
 <a href="lopban_1.html#K13" title="LOPBAN_1:func.13">modetrans</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font>
<b>by </b><i><a class="txt" href="lopban_2.html#E3:14"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="lopban_2.html#T6" target="_self" title="LOPBAN_2:th.6">Th6</a></i>
<br/>.= 
<font color="Maroon" title="c2">f</font>
<b>by </b><i><a class="ref" href="lopban_1.html#D12" title="LOPBAN_1:def.12">LOPBAN_1:def 12</a></i>
;<br/>


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