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<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="75_1_1_1"><span class="kw">now </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">  for <font color="Olive" title="b1">K1</font> being   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>   <a href="ec_pf_1.html#M1" title="EC_PF_1:mode.1">Subfield</a> of  <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a>  holds  <font color="Olive" title="b1">K1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a> </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">K1</font> be   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>   <a href="ec_pf_1.html#M1" title="EC_PF_1:mode.1">Subfield</a> of  <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</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"> <font color="Maroon" title="c3">K1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a> </span><br/><span class="kw">set </span><font color="Maroon" title="c4">C1</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">K1</font>;<br/><a NAME="E1:75_1_1_1"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">x</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a>  holds <br/><font color="Olive" title="b1">x</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c3">K1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gaussint.html#T25" target="_self" onmouseover="rs('gaussint/T25')" onmouseout="rh()">Th25</a></span>;<br/><a NAME="E2:75_1_1_1"/>
 <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a>  is   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>   <a href="ec_pf_1.html#M1" title="EC_PF_1:mode.1">Subfield</a> of  <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ec_pf_1.html#T1" onmouseover="rs('ec_pf_1/T1')" onmouseout="rh()">EC_PF_1:1</a></span>;<br/><a NAME="E3:75_1_1_1"/><span class="kw">then </span>
 <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a>  is   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>   <a href="ec_pf_1.html#M1" title="EC_PF_1:mode.1">Subfield</a> of <font color="Maroon" title="c3">K1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:75_1_1_1"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="ec_pf_1.html#T7" onmouseover="rs('ec_pf_1/T7')" onmouseout="rh()">EC_PF_1:7</a></span>;<br/><span class="kw">hence </span><a NAME="E4:75_1_1_1"/>
<font color="Maroon" title="c3">K1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ec_pf_1.html#T4" onmouseover="rs('ec_pf_1/T4')" onmouseout="rh()">EC_PF_1:4</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><span class="kw">end;</span></div>
<a NAME="E2:75_1_1"/><span class="kw">then </span>
 for <font color="Olive" title="b1">K1</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a>  st <font color="Olive" title="b1">K1</font> is   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>   <a href="ec_pf_1.html#M1" title="EC_PF_1:mode.1">Subfield</a> of  <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a>  holds <br/><font color="Olive" title="b1">K1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E3:75_1_1"/>
 <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a>  is  <a href="ec_pf_1.html#V1" title="EC_PF_1:attr.1">prime</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ec_pf_1.html#D2" onmouseover="rs('ec_pf_1/D2')" onmouseout="rh()">EC_PF_1:def 2</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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