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<a NAME="E1:88_2_1"/><span class="lab"><font color="Green" title="E47">A</font></span>: 
<font color="Maroon" title="c1">F</font> is    <a href="c0sp1.html#M1" title="C0SP1:mode.1">Subring</a> of <font color="Maroon" title="c2">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_4.html#D1" onmouseover="rs('field_4/D1')" onmouseout="rh()">FIELD_4:def 1</a></span>;<br/>
<a NAME="E2:88_2_1"/><span class="kw">then </span>
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c2">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="c0sp1.html#D3" onmouseover="rs('c0sp1/D3')" onmouseout="rh()">C0SP1:def 3</a></span>;<br/>
<a NAME="E3:88_2_1"/><span class="kw">then </span>
 <a href="struct_0.html#K9" title="STRUCT_0:func.9">In</a> (<span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c2">E</font></span>)</span>,<font color="Maroon" title="c2">E</font>) <a href="algnum_1.html#R1" title="ALGNUM_1:pred.1">is_integral_over</a> <font color="Maroon" title="c1">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:88_2_1"><span class="lab"><font color="Green" title="E47">A</font></span></a>, <a class="ref" href="algnum_1.html#T23" onmouseover="rs('algnum_1/T23')" onmouseout="rh()">ALGNUM_1:23</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:88_2_1"/>
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c2">E</font> is <font color="Maroon" title="c1">F</font> <a href="field_6.html#V2" title="FIELD_6:attr.2">-algebraic</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="field_6.html#T42" onmouseover="rs('field_6/T42')" onmouseout="rh()">FIELD_6:42</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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