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<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="87_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">o</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">E</font>  st <font color="Olive" title="b1">o</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="field_7.html#K1" title="FIELD_7:func.1">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="field_7.html#K1" title="FIELD_7:func.1">}</a></span> holds <br/><font color="Olive" title="b1">o</font> is <font color="Maroon" title="c1">F</font> <a href="field_6.html#V2" title="FIELD_6:attr.2">-algebraic</a> </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">o</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">E</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="c5">o</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="field_7.html#K1" title="FIELD_7:func.1">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="field_7.html#K1" title="FIELD_7:func.1">}</a></span> implies <font color="Olive">b<sub>1</sub></font> is <font color="Maroon" title="c1">F</font> <a href="field_6.html#V2" title="FIELD_6:attr.2">-algebraic</a>  )</span><br/><span class="kw">assume </span><a NAME="E1:87_1_1_1"/>
<font color="Maroon" title="c5">o</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="field_7.html#K1" title="FIELD_7:func.1">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="field_7.html#K1" title="FIELD_7:func.1">}</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"> <font color="Olive">b<sub>1</sub></font> is <font color="Maroon" title="c1">F</font> <a href="field_6.html#V2" title="FIELD_6:attr.2">-algebraic</a> </span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="87_1_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:87_1_1_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> or <font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="87_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:87_1_1_1_1_1"/>
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</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="Olive">b<sub>1</sub></font> is <font color="Maroon" title="c1">F</font> <a href="field_6.html#V2" title="FIELD_6:attr.2">-algebraic</a> </span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:87_1_1_1_1_1"/>
<font color="Maroon" title="c5">o</font> is <font color="Maroon" title="c1">F</font> <a href="field_6.html#V2" title="FIELD_6:attr.2">-algebraic</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"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="87_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:87_1_1_1_1_2"/>
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</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="Olive">b<sub>1</sub></font> is <font color="Maroon" title="c1">F</font> <a href="field_6.html#V2" title="FIELD_6:attr.2">-algebraic</a> </span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:87_1_1_1_1_2"/>
<font color="Maroon" title="c5">o</font> is <font color="Maroon" title="c1">F</font> <a href="field_6.html#V2" title="FIELD_6:attr.2">-algebraic</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"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<a NAME="E2:87_1_1"/><span class="kw">then </span>
<span class="p1"><a href="field_7.html#K1" title="FIELD_7:func.1">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="field_7.html#K1" title="FIELD_7:func.1">}</a></span> is <font color="Maroon" title="c1">F</font> <a href="field_7.html#V3" title="FIELD_7:attr.3">-algebraic</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E3:87_1_1"/>
 <a href="field_6.html#K6" title="FIELD_6:func.6">FAdj</a> (<font color="Maroon" title="c1">F</font>,<span class="p1"><a href="field_7.html#K1" title="FIELD_7:func.1">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="field_7.html#K1" title="FIELD_7:func.1">}</a></span>) is <font color="Maroon" title="c1">F</font> <a href="field_4.html#V2" title="FIELD_4:attr.2">-finite</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"> verum</span><br/>


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