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

<span class="kw">reconsider </span><font color="Maroon" title="c3">K</font> = <font color="Maroon" title="c2">E</font> as  <font color="Maroon" title="c1">F</font> <a href="field_4.html#V1" title="FIELD_4:attr.1">-extending</a>  <a href="field_4.html#NM4" title="FIELD_4:NM.4">FieldExtension</a> of <font color="Maroon" title="c1">F</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="field_4.html#T6" onmouseover="rs('field_4/T6')" onmouseout="rh()">FIELD_4:6</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c3">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"> <font color="Maroon" title="c3">K</font> is <font color="Maroon" title="c2">E</font> <a href="field_4.html#V2" title="FIELD_4:attr.2">-finite</a> </span><br/>

<a NAME="E2:31_1_1"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">K</font> <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 <font color="Maroon" title="c2">E</font>
 
;<br/>
<a NAME="E3:31_1_1"/><span class="kw">then </span>
 <a href="field_4.html#K3" title="FIELD_4:func.3">deg</a> (<font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c2">E</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_7.html#T7" target="_self" onmouseover="rs('field_7/T7')" onmouseout="rh()">quah1</a></span>;<br/>
<a NAME="E4:31_1_1"/><span class="kw">then </span>
<span class="p1"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c3">K</font></span>)</span></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span> is   <a href="vectsp_7.html#NM1" title="VECTSP_7:NM.1">Basis</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c2">E</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_7.html#T9" target="_self" onmouseover="rs('field_7/T9')" onmouseout="rh()">quah2</a></span>;<br/>
<a NAME="E5:31_1_1"/><span class="kw">then </span>
 <a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c2">E</font>) is  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D1" onmouseover="rs('matrlin/D1')" onmouseout="rh()">MATRLIN:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:31_1_1"/>
<font color="Maroon" title="c3">K</font> is <font color="Maroon" title="c2">E</font> <a href="field_4.html#V2" title="FIELD_4:attr.2">-finite</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="field_4.html#D8" onmouseover="rs('field_4/D8')" onmouseout="rh()">FIELD_4:def 8</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/>


</div>
