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<span class="kw">let </span><font color="Maroon" title="c1">E</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">  for <font color="Olive" title="b1">B</font>, <font color="Olive" title="b2">A</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span>  st <font color="Olive" title="b1">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a>  holds <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b2">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a></span>)</span> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <font color="Olive" title="b1">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a>  &amp; <font color="Olive" title="b1">B</font> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">A</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></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="c2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a>  implies ( <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a></span>)</span> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <font color="Maroon" title="c2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a>  &amp; <font color="Maroon" title="c2">B</font> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a>  ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:95"/><span class="lab"><font color="Green" title="E56">A1</font></span>: 
<font color="Maroon" title="c2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> 
 ; <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">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a></span>)</span> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <font color="Maroon" title="c2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a>  &amp; <font color="Maroon" title="c2">B</font> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a>  )</span><br/>

<a NAME="E2:95"/><span class="kw">then </span>
<font color="Maroon" title="c2">B</font> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a></span>)</span> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="flang_1.html#T17" title="FLANG_1:th.17">FLANG_1:17</a></span>;<br/>
<a NAME="E3:95"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A2</font></span>: 
<font color="Maroon" title="c2">B</font> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a></span>)</span> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="flang_3.html#T86" target="_self" title="FLANG_3:th.86">Th86</a></span>;<br/>
<a NAME="E4:95"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a></span>)</span> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <font color="Maroon" title="c2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a></span>)</span> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:95"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="ref" href="flang_1.html#T17" title="FLANG_1:th.17">FLANG_1:17</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:95"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a></span>)</span> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <font color="Maroon" title="c2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a>  &amp; <font color="Maroon" title="c2">B</font> <a href="flang_1.html#K6" title="FLANG_1:func.6">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> <a href="flang_3.html#K2" title="FLANG_3:func.2">+</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:95"><span class="lab"><font color="Green" title="E57">A2</font></span></a>, <a class="ref" href="flang_3.html#T92" target="_self" title="FLANG_3:th.92">Th92</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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