<?xml version="1.0"?>
<div class="add">

<a NAME="E1:42_1_1"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T7" onmouseover="rs('zfmisc_1/T7')" onmouseout="rh()">ZFMISC_1:7</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c1">A</font> = <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <span class="kw">by</span> <span class="lab"><a class="ref" href="finsub_1.html#D5" onmouseover="rs('finsub_1/D5')" onmouseout="rh()">FINSUB_1:def 5</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c2">x</font> =  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> , <font color="Maroon" title="c3">y</font> = 1 as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">R</font> =  the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">n</font> = (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="funct_4.html#K7" title="FUNCT_4:func.7">--&gt;</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font>) as   <a href="binop_1.html#NM1" title="BINOP_1:NM.1">UnOp</a> of <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">f</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of  the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>  <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">A</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">T</font> =  <a href="abcmiz_0.html#G2" title="ABCMIZ_0:aggr.2">TA-structure</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of  the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ,<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of  the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ,<font color="Maroon" title="c5">n</font>,<span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of  the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>  <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">A</font></span>)</span> #);<br/>
<a NAME="E5:42_1_1"/>
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="abcmiz_0.html#G2" title="ABCMIZ_0:aggr.2">TA-structure</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of  the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ,<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of  the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ,<font color="Maroon" title="c5">n</font>,<span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of  the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>  <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">A</font></span>)</span> #), the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <a href="abcmiz_0.html#G2" title="ABCMIZ_0:aggr.2">TA-structure</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of  the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ,<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of  the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ,<font color="Maroon" title="c5">n</font>,<span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of  the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>  <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">A</font></span>)</span> #) #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of  the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> , the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of  the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>  #)
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">T</font> =  <a href="abcmiz_0.html#G2" title="ABCMIZ_0:aggr.2">TA-structure</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of  the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ,<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of  the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ,<font color="Maroon" title="c5">n</font>,<span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of  the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>  <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">A</font></span>)</span> #) as  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="abcmiz_0.html#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D19" onmouseover="rs('struct_0/D19')" onmouseout="rh()">STRUCT_0:def 19</a>, <a class="ref" href="waybel_8.html#T12" onmouseover="rs('waybel_8/T12')" onmouseout="rh()">WAYBEL_8:12</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c8">T</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E7:42_1_1"/>
 not <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E8:42_1_1"/>
<font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>  )</span><br/>

<a NAME="E9:42_1_1"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
<font color="Maroon" title="c5">n</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T63" onmouseover="rs('funct_4/T63')" onmouseout="rh()">FUNCT_4:63</a></span>;<br/>
<a NAME="E10:42_1_1"/><span class="lab"><font color="Green" title="E22">A2</font></span>: 
<font color="Maroon" title="c5">n</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T63" onmouseover="rs('funct_4/T63')" onmouseout="rh()">FUNCT_4:63</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:42_1_1"/>
( <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:42_1_1"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="abcmiz_0.html#T4" target="_self" onmouseover="rs('abcmiz_0/T4')" onmouseout="rh()">Th4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>  )</span><br/>

<div><span class="kw">hereby </span> <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="abcmiz_0.html#D9" target="_self" onmouseover="rs('abcmiz_0/D9')" onmouseout="rh()">ABCMIZ_0:def 9</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>  &amp; <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>  )</span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c9">t</font> be   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c8">T</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="c8">T</font>  st <font color="Olive" title="b1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c9">t</font> holds <br/> not  <a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Olive" title="b1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c9">t</font></span><br/><span class="kw">let </span><font color="Maroon" title="c10">a</font> be   <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c8">T</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c9">t</font> implies  not  <a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c10">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c9">t</font> )</span><br/><a NAME="E1:42_1_1_1"/><span class="lab"><font color="Green" title="E23">A3</font></span>: 
 <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c9">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T7" onmouseover="rs('funcop_1/T7')" onmouseout="rh()">FUNCOP_1:7</a></span>;<br/><a NAME="E2:42_1_1_1"/>
( <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E3:42_1_1_1"/>
( <font color="Maroon" title="c10">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c9">t</font> implies  not  <a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c10">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c9">t</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:42_1_1"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="txt" href="#E1:42_1_1_1"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">set </span><font color="Maroon" title="c9">t</font> =  the   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c8">T</font>;<br/>
<div><span class="kw">hereby </span> <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="abcmiz_0.html#D11" target="_self" onmouseover="rs('abcmiz_0/D11')" onmouseout="rh()">ABCMIZ_0:def 11</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c8">T</font> is  <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a> </span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c10">t1</font>, <font color="Maroon" title="c11">t2</font> be   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c8">T</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">t1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c11">t2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c10">t1</font></span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c11">t2</font></span>)</span></span><br/><a NAME="E1:42_1_1_2"/><span class="lab"><font color="Green" title="E23">A4</font></span>: 
 <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c11">t2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T7" onmouseover="rs('funcop_1/T7')" onmouseout="rh()">FUNCOP_1:7</a></span>;<br/><a NAME="E2:42_1_1_2"/>
 <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c10">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T7" onmouseover="rs('funcop_1/T7')" onmouseout="rh()">FUNCOP_1:7</a></span>;<br/><span class="kw">hence </span><a NAME="E3:42_1_1_2"/>
 <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">t1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c11">t2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c10">t1</font></span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c11">t2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1_1_2"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="ref" href="funcop_1.html#T7" onmouseover="rs('funcop_1/T7')" onmouseout="rh()">FUNCOP_1:7</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c10">a</font> be   <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c8">T</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="abcmiz_0.html#D14" target="_self" onmouseover="rs('abcmiz_0/D14')" onmouseout="rh()">ABCMIZ_0:def 14</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <span class="p1">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <span class="p2">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c10">a</font></span>)</span></span>)</span> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/>

<a NAME="E14:42_1_1"/><span class="lab"><font color="Green" title="E23">A5</font></span>: 
 <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a>  the   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c8">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T7" onmouseover="rs('funcop_1/T7')" onmouseout="rh()">FUNCOP_1:7</a></span>;<br/>
<a NAME="E15:42_1_1"/>
( <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/>
<a NAME="E16:42_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c10">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a>  the   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c8">T</font> or  <a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c10">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a>  the   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c8">T</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:42_1_1"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="txt" href="#E14:42_1_1"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<a NAME="E17:42_1_1"/><span class="kw">then </span>
(  the   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c8">T</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c10">a</font> or  the   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c8">T</font> <a href="tarski.html#R2" title="TARSKI: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="c10">a</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#T13" target="_self" onmouseover="rs('abcmiz_0/T13')" onmouseout="rh()">Th13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E18:42_1_1"/>
 not <span class="p1">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <span class="p2">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c10">a</font></span>)</span></span>)</span> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
