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<span class="kw">let </span><font color="Maroon" title="c1">Y</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">S</font> being   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b2">D</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">X</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b3">X</font> is <font color="Olive" title="b2">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  holds <br/><font color="Maroon" title="c1">Y</font> is <font color="Olive" title="b2">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</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">D</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c2">S</font><br/>  for <font color="Olive" title="b2">X</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b2">X</font> is <font color="Olive" title="b1">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  holds <br/><font color="Maroon" title="c1">Y</font> is <font color="Olive" title="b1">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">D</font> be   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c2">S</font>; <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">X</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b1">X</font> is <font color="Maroon" title="c3">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  holds <br/><font color="Maroon" title="c1">Y</font> is <font color="Maroon" title="c3">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">X</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</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="c4">X</font> is <font color="Maroon" title="c3">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  implies <font color="Maroon" title="c1">Y</font> is <font color="Maroon" title="c3">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">N</font> =  <a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">assume </span><a NAME="E1:185"/>
<font color="Maroon" title="c4">X</font> is <font color="Maroon" title="c3">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</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="c1">Y</font> is <font color="Maroon" title="c3">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">phi1</font>, <font color="Maroon" title="c7">phi2</font> being   <a href="fomodel2.html#V4" title="FOMODEL2:attr.4">wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c2">S</font><span class="kw"> such that </span><br/><a NAME="E3:185"/><span class="lab"><font color="Green" title="E103">B0</font></span>: 
( <font color="Maroon" title="c6">phi1</font> is <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c3">D</font> <a href="fomodel4.html#V8" title="FOMODEL4:attr.8">-provable</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c6">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c7">phi2</font> is <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c3">D</font> <a href="fomodel4.html#V8" title="FOMODEL4:attr.8">-provable</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D65" target="_self" title="FOMODEL4:def.65">DefInc</a></span>;<br/>
<span class="kw">thus </span><a NAME="E4:185"/>
<font color="Maroon" title="c1">Y</font> is <font color="Maroon" title="c3">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D65" target="_self" title="FOMODEL4:def.65">DefInc</a>, <a class="txt" href="#E3:185"><span class="lab"><font color="Green" title="E103">B0</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/>


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