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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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#K10" title="AFINSQ_1:func.10">^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/><b>let </b><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#K10" title="AFINSQ_1:func.10">^omega</a> </span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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/>





<b>assume </b><a NAME="E1:95"/>
<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:()"><i><font color="Red">::  thesis: </font></i></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"/><b>then </b>
( <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> &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> <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> )
 
<b>by </b><i><a class="ref" href="flang_1.html#T18" title="FLANG_1:th.18">FLANG_1:18</a></i>;<br/>
<a NAME="E3:95"/><b>then </b>
( <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> &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> <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> )
 
<b>by </b><i><a class="ref" href="flang_3.html#T86" target="_self" title="FLANG_3:th.86">Th86</a></i>;<br/>
<b>hence </b><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> <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>  )
 <b>by </b><i><a class="ref" href="flang_3.html#T92" target="_self" title="FLANG_3:th.92">Th92</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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