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<span class="kw">consider </span><font color="Maroon" title="c3">A</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E2:25_1_1"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
 <a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_1.html#G1" title="VECTSP_1:aggr.1">ModuleStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">V</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c1">V</font>, the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">lmult</a> of <font color="Maroon" title="c1">V</font> #)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zmodul03.html#D4" onmouseover="rs('zmodul03/D4')" onmouseout="rh()">ZMODUL03:def 4</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">T</font> =  <a href="zmodul07.html#K2" title="ZMODUL07:func.2">ZQMorph</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">W</font>);<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">B</font> = <span class="p1">(<span class="default"><a href="zmodul07.html#K2" title="ZMODUL07:func.2">ZQMorph</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">W</font>)</span>)</span> <a href="ranknull.html#K2" title="RANKNULL:func.2">.:</a> <font color="Maroon" title="c3">A</font> as   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">W</font>)</span>)</span> ;<br/>
<a NAME="E4:25_1_1"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<span class="p1">(<span class="default"><a href="zmodul07.html#K2" title="ZMODUL07:func.2">ZQMorph</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">W</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zmodul06.html#T40" onmouseover="rs('zmodul06/T40')" onmouseout="rh()">ZMODUL06:40</a></span>;<br/>
<a NAME="E5:25_1_1"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="zmodul07.html#K2" title="ZMODUL07:func.2">ZQMorph</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">W</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">W</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D3" onmouseover="rs('funct_2/D3')" onmouseout="rh()">FUNCT_2:def 3</a></span>;<br/>
<span class="lab"><font color="Green" title="E18">X1</font></span>:  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="zmodul07.html#K2" title="ZMODUL07:func.2">ZQMorph</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">W</font>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="zmodul07.html#K2" title="ZMODUL07:func.2">ZQMorph</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">W</font>)</span>)</span> <a href="ranknull.html#K2" title="RANKNULL:func.2">.:</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="zmodul07.html#K2" title="ZMODUL07:func.2">ZQMorph</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">W</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T113" onmouseover="rs('relat_1/T113')" onmouseout="rh()">RELAT_1:113</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="zmodul07.html#K2" title="ZMODUL07:func.2">ZQMorph</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">W</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <font color="Maroon" title="c3">A</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:25_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>
;<br/>
<a NAME="E7:25_1_1"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <font color="Maroon" title="c5">B</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">W</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_4.html#D2" onmouseover="rs('vectsp_4/D2')" onmouseout="rh()">VECTSP_4:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:25_1_1"/>
 <a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">W</font>) is  <a href="zmodul03.html#V2" title="ZMODUL03:attr.2">finitely-generated</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:25_1_1"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E5:25_1_1"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E6:25_1_1"><span class="lab"><font color="Green" title="E18">X1</font></span></a>, <a class="ref" href="xboole_0.html#D10" onmouseover="rs('xboole_0/D10')" onmouseout="rh()">XBOOLE_0:def 10</a>, <a class="ref" href="zmodul01.html#T47" onmouseover="rs('zmodul01/T47')" onmouseout="rh()">ZMODUL01:47</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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