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<span class="kw">consider </span><font color="Maroon" title="c3">J</font> being   <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <span class="p1">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">X</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:23_1_1"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<font color="Maroon" title="c3">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">I</font> <a href="lopban14.html#K4" title="LOPBAN14:func.4">"</a> 
 <span class="kw">and </span><br/><a NAME="E3:23_1_1"/><span class="lab"><font color="Green" title="E12">A2</font></span>: 
( <font color="Maroon" title="c3">J</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Maroon" title="c3">J</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  )
 <span class="kw">and </span><br/><a NAME="E4:23_1_1"/><span class="lab"><font color="Green" title="E13">A3</font></span>: 
<font color="Maroon" title="c3">J</font> is  <a href="mazurulm.html#V1" title="MAZURULM:attr.1">isometric</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ndiff_7.html#T9" onmouseover="rs('ndiff_7/T9')" onmouseout="rh()">NDIFF_7:9</a></span>;<br/>
<span class="kw">thus </span><a NAME="E5:23_1_1"/>
 for <font color="Olive">b<sub>1</sub></font> being   <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <span class="p1">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">X</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c1">X</font>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">I</font> <a href="lopban14.html#K4" title="LOPBAN14:func.4">"</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Olive">b<sub>1</sub></font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  &amp; <font color="Olive">b<sub>1</sub></font> is  <a href="mazurulm.html#V1" title="MAZURULM:attr.1">isometric</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23_1_1"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E3:23_1_1"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="txt" href="#E4:23_1_1"><span class="lab"><font color="Green" title="E13">A3</font></span></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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