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<b>let </b><font color="Maroon" title="c1">T</font> be  <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>  <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</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">a</font> being  <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c1">T</font> holds   <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Olive" title="b1">a</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Olive" title="b1">a</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">a</font> be   <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c2">a</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c2">a</font></span>)</span></span><br/>



<b>assume </b><a NAME="E1:44"/>
 <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c2">a</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c2">a</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>then consider </b><font color="Maroon" title="c3">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:44"/><i><font color="Green" title="E21">A1</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c2">a</font>
 <b>and </b><br/><a NAME="E4:44"/><i><font color="Green" title="E22">A2</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c2">a</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">t1</font> being   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E6:44"/><i><font color="Green" title="E23">A3</font></i>: 
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t1</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c4">t1</font> )
 <b>by </b><i><a class="txt" href="#E3:44"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="abcmiz_0.html#D12" target="_self" title="ABCMIZ_0:def.12">Def12</a></i>;<br/>
<a NAME="E7:44"/>
 ex <font color="Olive" title="b1">t2</font> being  <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">t2</font> &amp;  <a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Olive" title="b1">t2</font> )
 
<b>by </b><i><a class="txt" href="#E4:44"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="abcmiz_0.html#D12" target="_self" title="ABCMIZ_0:def.12">Def12</a></i>;<br/>
<b>hence </b><a NAME="E8:44"/>
contradiction
 <b>by </b><i><a class="txt" href="#E6:44"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="abcmiz_0.html#D9" target="_self" title="ABCMIZ_0:def.9">Def9</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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