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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#L4" title="ALGSTR_0:struct.4">multLoopStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">I</font>, <font color="Olive" title="b2">J</font>, <font color="Olive" title="b3">K</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">J</font> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <font color="Olive" title="b3">K</font></span>)</span> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">J</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">K</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Olive" title="b1">I</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">I</font>, <font color="Maroon" title="c3">J</font>, <font color="Maroon" title="c4">K</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <font color="Maroon" title="c4">K</font></span>)</span> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">K</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font></span>)</span></span><br/>



<div><span class="lab"><font color="Green" title="E58">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="142_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">u</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <font color="Maroon" title="c4">K</font></span>)</span> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font> implies <font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">K</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:142_1"/>
<font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <font color="Maroon" title="c4">K</font></span>)</span> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">K</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font></span>)</span></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font><span class="kw"> such that </span><br/><a NAME="E3:142_1"/><span class="lab"><font color="Green" title="E59">A2</font></span>: 
<font color="Maroon" title="c5">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a</font>
 <span class="kw">and </span><br/><a NAME="E4:142_1"/><span class="lab"><font color="Green" title="E60">A3</font></span>: 
<font color="Maroon" title="c6">a</font> <a href="ideal_1.html#K10" title="IDEAL_1:func.10">*</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <font color="Maroon" title="c4">K</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="142_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">v</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">a</font> <a href="ideal_1.html#K10" title="IDEAL_1:func.10">*</a> <font color="Maroon" title="c2">I</font> implies <font color="Maroon" title="c7">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">K</font> )</span><br/><span class="kw">assume </span><a NAME="E1:142_1_1"/>
<font color="Maroon" title="c7">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">a</font> <a href="ideal_1.html#K10" title="IDEAL_1:func.10">*</a> <font color="Maroon" title="c2">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">K</font></span><br/><a NAME="E2:142_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <font color="Maroon" title="c4">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:142_1"><span class="lab"><font color="Green" title="E60">A3</font></span></a></span>;<br/><a NAME="E3:142_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> st <br/>( <font color="Maroon" title="c7">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">K</font> )
 ;<br/><span class="kw">hence </span><a NAME="E4:142_1_1"/>
<font color="Maroon" title="c7">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">K</font>
 ; <a class="txt" 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="E6:142_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font> <a href="ideal_1.html#K10" title="IDEAL_1:func.10">*</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">K</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/><a NAME="E7:142_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A4</font></span>: 
<font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">K</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:142_1"><span class="lab"><font color="Green" title="E59">A2</font></span></a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="142_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">v</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">a</font> <a href="ideal_1.html#K10" title="IDEAL_1:func.10">*</a> <font color="Maroon" title="c2">I</font> implies <font color="Maroon" title="c7">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font> )</span><br/><span class="kw">assume </span><a NAME="E1:142_1_2"/>
<font color="Maroon" title="c7">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">a</font> <a href="ideal_1.html#K10" title="IDEAL_1:func.10">*</a> <font color="Maroon" title="c2">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font></span><br/><a NAME="E2:142_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <font color="Maroon" title="c4">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:142_1"><span class="lab"><font color="Green" title="E60">A3</font></span></a></span>;<br/><a NAME="E3:142_1_2"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> st <br/>( <font color="Maroon" title="c7">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">K</font> )
 ;<br/><span class="kw">hence </span><a NAME="E4:142_1_2"/>
<font color="Maroon" title="c7">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font>
 ; <a class="txt" 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="E9:142_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font> <a href="ideal_1.html#K10" title="IDEAL_1:func.10">*</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">J</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/><a NAME="E10:142_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:142_1"><span class="lab"><font color="Green" title="E59">A2</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E11:142_1"/>
<font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">K</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:142_1"><span class="lab"><font color="Green" title="E61">A4</font></span></a></span>; <a class="txt" 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="hs2(this)" href="javascript:()" title="142_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">u</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">K</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font></span>)</span> implies <font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <font color="Maroon" title="c4">K</font></span>)</span> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font> )</span><br/><span class="kw">assume </span><a NAME="E1:142_2"/>
<font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">K</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <font color="Maroon" title="c4">K</font></span>)</span> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font></span><br/><a NAME="E2:142_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A5</font></span>: 
 ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">K</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font> )
 ;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font><span class="kw"> such that </span><br/><a NAME="E4:142_2"/><span class="lab"><font color="Green" title="E60">A6</font></span>: 
<font color="Maroon" title="c5">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a</font>
 <span class="kw">and </span><br/><a NAME="E5:142_2"/><span class="lab"><font color="Green" title="E61">A7</font></span>: 
<font color="Maroon" title="c6">a</font> <a href="ideal_1.html#K10" title="IDEAL_1:func.10">*</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">J</font>
 ;<br/><a NAME="E6:142_2"/>
 ex <font color="Olive" title="b1">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> st <br/>( <font color="Maroon" title="c5">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> &amp; <font color="Olive" title="b1">b</font> <a href="ideal_1.html#K10" title="IDEAL_1:func.10">*</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">K</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:142_2"><span class="lab"><font color="Green" title="E59">A5</font></span></a></span>;<br/><a NAME="E7:142_2"/><span class="kw">then </span>
 for <font color="Olive" title="b1">v</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">a</font> <a href="ideal_1.html#K10" title="IDEAL_1:func.10">*</a> <font color="Maroon" title="c2">I</font> holds <br/><font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <font color="Maroon" title="c4">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:142_2"><span class="lab"><font color="Green" title="E60">A6</font></span></a>, <a class="txt" href="#E5:142_2"><span class="lab"><font color="Green" title="E61">A7</font></span></a></span>;<br/><a NAME="E8:142_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font> <a href="ideal_1.html#K10" title="IDEAL_1:func.10">*</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <font color="Maroon" title="c4">K</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E9:142_2"/>
<font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <font color="Maroon" title="c4">K</font></span>)</span> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:142_2"><span class="lab"><font color="Green" title="E60">A6</font></span></a></span>; <a class="txt" 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>
<span class="kw">hence </span><a NAME="E3:142"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <font color="Maroon" title="c4">K</font></span>)</span> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">K</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <font color="Maroon" title="c2">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:142"><span class="lab"><font color="Green" title="E58">A1</font></span></a>, <a class="ref" href="tarski.html#T1" title="TARSKI:th.1">TARSKI:1</a></span>; <a class="txt" 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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