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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="struct_0.html#M1">Element</a> of  <a href="lopban_1.html#K10">BoundedLinearOperators</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:14"/><i><font color="Green">E9</font></i>: 
<span class="p1">(<span class="default"><a href="lopban_1.html#K13">modetrans</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lopban_2.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><a href="lopban_1.html#K13">modetrans</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> is    <a href="struct_0.html#M1">Element</a> of  <a href="lopban_1.html#K10">BoundedLinearOperators</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="lopban_1.html#D10">LOPBAN_1:def 10</a></i>;<br/>
 <a href="lopban_1.html#K13">modetrans</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lopban_2.html#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font> = 
 <a href="lopban_1.html#K13">modetrans</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lopban_1.html#K13">modetrans</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lopban_2.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><a href="lopban_1.html#K13">modetrans</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>

<br/>.= 
<span class="p1">(<span class="default"><a href="lopban_1.html#K13">modetrans</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lopban_2.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><a href="lopban_1.html#K13">modetrans</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="lopban_2.html#E1:14"><i><font color="Green">E9</font></i></a>, <a class="ref" href="lopban_1.html#D12">LOPBAN_1:def 12</a></i>
;<br/>
<a NAME="E3:14"/><b>then </b><i><font color="Green">E10</font></i>: 
<span class="p1">(<span class="default"><a href="lopban_1.html#K13">modetrans</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lopban_2.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><a href="lopban_1.html#K13">modetrans</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lopban_2.html#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lopban_1.html#K13">modetrans</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lopban_2.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><a href="lopban_1.html#K13">modetrans</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="lopban_2.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><a href="lopban_1.html#K13">modetrans</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="lopban_2.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E4:14"/><i><font color="Green">E11</font></i>: 
<span class="p1">(<span class="default"><a href="lopban_1.html#K13">modetrans</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lopban_2.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><a href="lopban_1.html#K13">modetrans</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> is    <a href="struct_0.html#M1">Element</a> of  <a href="lopban_1.html#K10">BoundedLinearOperators</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="lopban_1.html#D10">LOPBAN_1:def 10</a></i>;<br/>
 <a href="lopban_1.html#K13">modetrans</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lopban_2.html#K4" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font> = 
 <a href="lopban_1.html#K13">modetrans</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lopban_1.html#K13">modetrans</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lopban_2.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><a href="lopban_1.html#K13">modetrans</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>

<br/>.= 
<span class="p1">(<span class="default"><a href="lopban_1.html#K13">modetrans</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lopban_2.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><a href="lopban_1.html#K13">modetrans</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="lopban_2.html#E4:14"><i><font color="Green">E11</font></i></a>, <a class="ref" href="lopban_1.html#D12">LOPBAN_1:def 12</a></i>
;<br/>
<b>hence </b><a NAME="E6:14"/>
<font color="Maroon">c<sub>2</sub></font> <a href="lopban_2.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lopban_2.html#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lopban_2.html#K4" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="lopban_2.html#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="lopban_2.html#E3:14"><i><font color="Green">E10</font></i></a></i>;<br/>


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