<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="clvect_1.html#NM5">ComplexNormSpace</a>;<br/>

<a NAME="E1:25"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="clopban2.html#K7" target="_self">Ring_of_BoundedLinearOperators</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>3</sub></font></span>)</span> &amp; <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <span class="p2">(<span class="default"><a href="clopban2.html#K7" target="_self">Ring_of_BoundedLinearOperators</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; ex <font color="Olive">b<sub>4</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="clopban2.html#K7" target="_self">Ring_of_BoundedLinearOperators</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><a href="clopban2.html#K7" target="_self">Ring_of_BoundedLinearOperators</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span> &amp; <font color="Olive">b<sub>1</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <span class="p2">(<span class="default"><a href="clopban2.html#K7" target="_self">Ring_of_BoundedLinearOperators</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <span class="p2">(<span class="default"><a href="clopban2.html#K7" target="_self">Ring_of_BoundedLinearOperators</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="clopban2.html#T13" target="_self">Th13</a></i>;<br/>
<b>hence </b><a NAME="E2:25"/>
 <a href="clopban2.html#K7" target="_self">Ring_of_BoundedLinearOperators</a> <font color="Maroon">c<sub>1</sub></font> is   <a href="funcsdom.html#NM1">Ring</a>
 <b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a>, <a class="ref" href="rlvect_1.html#D5">RLVECT_1:def 5</a>, <a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a>, <a class="ref" href="rlvect_1.html#D7">RLVECT_1:def 7</a>, <a class="ref" href="rlvect_1.html#D8">RLVECT_1:def 8</a>, <a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a>, <a class="ref" href="vectsp_1.html#D18">VECTSP_1:def 18</a>, <a class="ref" href="vectsp_1.html#D19">VECTSP_1:def 19</a></i>;<br/>


</div>
