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<span class="kw">let </span><font color="Maroon" title="c1">K</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</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">V</font> being   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Maroon" title="c1">K</font>  ex <font color="Olive" title="b2">T</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b1">V</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b1">V</font></span>)</span> <a href="prvect_1.html#K6" title="PRVECT_1:func.6">-VectSp_over</a> <font color="Maroon" title="c1">K</font></span>)</span> st <font color="Olive" title="b2">T</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Maroon" title="c1">K</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">  ex <font color="Olive" title="b1">T</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c2">V</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="prvect_1.html#K6" title="PRVECT_1:func.6">-VectSp_over</a> <font color="Maroon" title="c1">K</font></span>)</span> st <font color="Olive" title="b1">T</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> </span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">b</font> =  the    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c2">V</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">W</font> = <span class="p1">(<span class="default"><a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="prvect_1.html#K6" title="PRVECT_1:func.6">-VectSp_over</a> <font color="Maroon" title="c1">K</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">W0</font> = <span class="p1">(<span class="default"><a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="prvect_1.html#K4" title="PRVECT_1:func.4">-Group_over</a> <font color="Maroon" title="c1">K</font>;<br/>
<a NAME="E1:61"/>
 ex <font color="Olive" title="b1">T</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c2">V</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="prvect_1.html#K6" title="PRVECT_1:func.6">-VectSp_over</a> <font color="Maroon" title="c1">K</font></span>)</span> st <br/>( <font color="Olive" title="b1">T</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  &amp; (  for <font color="Olive" title="b2">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">V</font> holds  <font color="Olive" title="b1">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a>  the    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c2">V</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="real_ns2.html#T63" target="_self" onmouseover="rs('real_ns2/T63')" onmouseout="rh()">Th63</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:61"/>
 ex <font color="Olive" title="b1">T</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c2">V</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="prvect_1.html#K6" title="PRVECT_1:func.6">-VectSp_over</a> <font color="Maroon" title="c1">K</font></span>)</span> st <font color="Olive" title="b1">T</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</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"> verum</span><br/>


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