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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">K1</font> being    <a href="ec_pf_1.html#M1" title="EC_PF_1:mode.1">Subfield</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b4">x1</font>, <font color="Olive" title="b5">y1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">K1</font>  st <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">x1</font> &amp; <font color="Olive" title="b2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font> holds <br/><font color="Olive" title="b2">x</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">x1</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">K1</font> be    <a href="ec_pf_1.html#M1" title="EC_PF_1:mode.1">Subfield</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">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b3">x1</font>, <font color="Olive" title="b4">y1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">K1</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">x1</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font> holds <br/><font color="Olive" title="b1">x</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">x1</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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">  for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">y1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">K1</font>  st <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x1</font> &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font> holds <br/><font color="Maroon" title="c3">x</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x1</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c5">x1</font>, <font color="Maroon" title="c6">y1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">K1</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">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x1</font> &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font> implies <font color="Maroon" title="c3">x</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x1</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c7">C</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">K</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">C1</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">K1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">hpd</font> = <font color="Maroon" title="c5">x1</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a> ;<br/>
<span class="kw">assume </span><a NAME="E1:69"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x1</font> &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <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"> <font color="Maroon" title="c3">x</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x1</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a> </span><br/>

<a NAME="E2:69"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A2</font></span>: 
<font color="Maroon" title="c5">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ec_pf_1.html#D1" onmouseover="rs('ec_pf_1/D1')" onmouseout="rh()">EC_PF_1:def 1</a></span>;<br/>
<a NAME="E3:69"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">K1</font> <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 <font color="Maroon" title="c1">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ec_pf_1.html#D1" onmouseover="rs('ec_pf_1/D1')" onmouseout="rh()">EC_PF_1:def 1</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">g</font> = <font color="Maroon" title="c5">x1</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font> ;<br/>
<span class="lab"><font color="Green" title="E29">A3</font></span>: <font color="Maroon" title="c3">x</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c10">g</font> = 
<font color="Maroon" title="c5">x1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="gaussint.html#T18" target="_self" onmouseover="rs('gaussint/T18')" onmouseout="rh()">Th18</a></span>
<br/>.= 
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c2">K1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:69"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="ref" href="vectsp_1.html#D10" onmouseover="rs('vectsp_1/D10')" onmouseout="rh()">VECTSP_1:def 10</a></span>
;<br/>
<a NAME="E6:69"/>
<font color="Maroon" title="c3">x</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c10">g</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">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:69"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="ec_pf_1.html#D1" onmouseover="rs('ec_pf_1/D1')" onmouseout="rh()">EC_PF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:69"/>
<font color="Maroon" title="c3">x</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x1</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="vectsp_1.html#D10" onmouseover="rs('vectsp_1/D10')" onmouseout="rh()">VECTSP_1:def 10</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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