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<span class="kw">let </span><font color="Maroon" title="c1">C</font> be   <a href="abcmiz_1.html#V3" title="ABCMIZ_1:attr.3">initialized</a>   <a href="abcmiz_a.html#V1" title="ABCMIZ_A:attr.1">standardized</a>  <a href="abcmiz_1.html#NM5" title="ABCMIZ_1:NM.5">ConstructorSignature</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="abcmiz_1.html#NM10" title="ABCMIZ_1:NM.10">quasi-adjective</a> of <font color="Maroon" title="c1">C</font> holds <br/> ( <font color="Olive" title="b1">a</font> is  <a href="abcmiz_1.html#V7" title="ABCMIZ_1:attr.7">negative</a>  iff <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K10" title="ABCMIZ_1:func.10">non_op</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">t</font> be   <a href="abcmiz_1.html#NM10" title="ABCMIZ_1:NM.10">quasi-adjective</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">t</font> is  <a href="abcmiz_1.html#V7" title="ABCMIZ_1:attr.7">negative</a>  iff <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K10" title="ABCMIZ_1:func.10">non_op</a>  )</span><br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:38_1"/>
( <font color="Maroon" title="c2">t</font> is   <a href="abcmiz_1.html#V6" title="ABCMIZ_1:attr.6">positive</a>   <a href="abcmiz_1.html#M1" title="ABCMIZ_1:mode.1">expression</a> of <font color="Maroon" title="c1">C</font>, <a href="abcmiz_1.html#K13" title="ABCMIZ_1:func.13">an_Adj</a> <font color="Maroon" title="c1">C</font> or <font color="Maroon" title="c2">t</font> is   <a href="abcmiz_1.html#V7" title="ABCMIZ_1:attr.7">negative</a>   <a href="abcmiz_1.html#M1" title="ABCMIZ_1:mode.1">expression</a> of <font color="Maroon" title="c1">C</font>, <a href="abcmiz_1.html#K13" title="ABCMIZ_1:func.13">an_Adj</a> <font color="Maroon" title="c1">C</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1_1"><span class="kw">suppose </span></a><a NAME="E1:38_1_1"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
<font color="Maroon" title="c2">t</font> is   <a href="abcmiz_1.html#V6" title="ABCMIZ_1:attr.6">positive</a>   <a href="abcmiz_1.html#M1" title="ABCMIZ_1:mode.1">expression</a> of <font color="Maroon" title="c1">C</font>, <a href="abcmiz_1.html#K13" title="ABCMIZ_1:func.13">an_Adj</a> <font color="Maroon" title="c1">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">t</font> is  <a href="abcmiz_1.html#V7" title="ABCMIZ_1:attr.7">negative</a>  iff <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K10" title="ABCMIZ_1:func.10">non_op</a>  )</span><br/><div class="add"><a NAME="E2:38_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_1.html#K20" title="ABCMIZ_1:func.20">Constructors</a>  &amp;  <a href="abcmiz_1.html#K10" title="ABCMIZ_1:func.10">non_op</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="abcmiz_1.html#K9" title="ABCMIZ_1:func.9">*</a> ,<a href="abcmiz_1.html#K10" title="ABCMIZ_1:func.10">non_op</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_a.html#T24" target="_self" title="ABCMIZ_A:th.24">Th57</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E3:38_1_1"/>
( <font color="Maroon" title="c2">t</font> is  <a href="abcmiz_1.html#V7" title="ABCMIZ_1:attr.7">negative</a>  iff <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K10" title="ABCMIZ_1:func.10">non_op</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38_1_1"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a>, <a class="ref" href="abcmiz_1.html#T39" title="ABCMIZ_1:th.39">ABCMIZ_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1_2"><span class="kw">suppose </span></a><a NAME="E1:38_1_2"/><span class="lab"><font color="Green" title="E20">B1</font></span>: 
<font color="Maroon" title="c2">t</font> is   <a href="abcmiz_1.html#V7" title="ABCMIZ_1:attr.7">negative</a>   <a href="abcmiz_1.html#M1" title="ABCMIZ_1:mode.1">expression</a> of <font color="Maroon" title="c1">C</font>, <a href="abcmiz_1.html#K13" title="ABCMIZ_1:func.13">an_Adj</a> <font color="Maroon" title="c1">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">t</font> is  <a href="abcmiz_1.html#V7" title="ABCMIZ_1:attr.7">negative</a>  iff <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K10" title="ABCMIZ_1:func.10">non_op</a>  )</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">a</font> being    <a href="abcmiz_1.html#M1" title="ABCMIZ_1:mode.1">expression</a> of <font color="Maroon" title="c1">C</font>, <a href="abcmiz_1.html#K13" title="ABCMIZ_1:func.13">an_Adj</a> <font color="Maroon" title="c1">C</font><span class="kw"> such that </span><br/><a NAME="E3:38_1_2"/><span class="lab"><font color="Green" title="E21">B2</font></span>: 
( <font color="Maroon" title="c3">a</font> is  <a href="abcmiz_1.html#V6" title="ABCMIZ_1:attr.6">positive</a>  &amp; <font color="Maroon" title="c2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="abcmiz_1.html#K32" title="ABCMIZ_1:func.32">non_op</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K30" title="ABCMIZ_1:func.30">term</a> <font color="Maroon" title="c3">a</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_1.html#D38" title="ABCMIZ_1:def.38">ABCMIZ_1:def 38</a></span>;<br/><a NAME="E4:38_1_2"/>
<font color="Maroon" title="c2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="abcmiz_1.html#K10" title="ABCMIZ_1:func.10">non_op</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">a</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:38_1_2"><span class="lab"><font color="Green" title="E21">B2</font></span></a>, <a class="ref" href="abcmiz_1.html#T43" title="ABCMIZ_1:th.43">ABCMIZ_1:43</a></span>;<br/><a NAME="E5:38_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="abcmiz_1.html#K10" title="ABCMIZ_1:func.10">non_op</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="trees_4.html#D4" title="TREES_4:def.4">TREES_4:def 4</a></span>;<br/><span class="kw">hence </span><a NAME="E6:38_1_2"/>
( <font color="Maroon" title="c2">t</font> is  <a href="abcmiz_1.html#V7" title="ABCMIZ_1:attr.7">negative</a>  iff <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K10" title="ABCMIZ_1:func.10">non_op</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38_1_2"><span class="lab"><font color="Green" title="E20">B1</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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