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<b>consider </b><font color="Maroon">R</font> being  non <a href="struct_0.html#V3">empty</a> <a href="realset2.html#V3">trivial</a> <a href="orders_2.html#V2">reflexive</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>
<b>reconsider </b><font color="Maroon">x</font> = 0, <font color="Maroon">y</font> = 1 as    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span> <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">n</font> = 0,1 <a href="funct_4.html#K5">--&gt;</a> <font color="Maroon">y</font>,<font color="Maroon">x</font> as   <a href="binop_1.html#NM1">UnOp</a> of <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span> ;<br/>
<a NAME="E4:43_1_1"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T12">ZFMISC_1:12</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">A</font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span> as    <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span> <b>by </b><i><a class="ref" href="finsub_1.html#D5">FINSUB_1:def 5</a></i>;<br/>
<b>set </b><font color="Maroon">f</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> <a href="borsuk_1.html#K1">--&gt;</a> <font color="Maroon">A</font>;<br/>
<b>set </b><font color="Maroon">T</font> =  <a href="abcmiz_0.html#G2" target="_self">TA-structure</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R</font>,<font color="Maroon">n</font>,<span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> <a href="borsuk_1.html#K1">--&gt;</a> <font color="Maroon">A</font></span>)</span> #);<br/>
<a NAME="E6:43_1_1"/>
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <a href="abcmiz_0.html#G2" target="_self">TA-structure</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R</font>,<font color="Maroon">n</font>,<span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> <a href="borsuk_1.html#K1">--&gt;</a> <font color="Maroon">A</font></span>)</span> #),the <a href="orders_2.html#U1">InternalRel</a> of <a href="abcmiz_0.html#G2" target="_self">TA-structure</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R</font>,<font color="Maroon">n</font>,<span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> <a href="borsuk_1.html#K1">--&gt;</a> <font color="Maroon">A</font></span>)</span> #) #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R</font> #)
 
;<br/>
<b>then reconsider </b><font color="Maroon">T</font> =  <a href="abcmiz_0.html#G2" target="_self">TA-structure</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R</font>,<font color="Maroon">n</font>,<span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> <a href="borsuk_1.html#K1">--&gt;</a> <font color="Maroon">A</font></span>)</span> #) as  non <a href="struct_0.html#V3">empty</a> <a href="realset2.html#V3">trivial</a> <a href="orders_2.html#V2">reflexive</a> <a href="abcmiz_0.html#V7" target="_self">strict</a>  <a href="abcmiz_0.html#L2" target="_self">TA-structure</a>  <b>by </b><i><a class="ref" href="tex_2.html#T4">TEX_2:4</a>, <a class="ref" href="waybel_8.html#T12">WAYBEL_8:12</a></i>;<br/>
<b>take </b>
<font color="Maroon">T</font>
;<br/>

<b>thus </b><a NAME="E8:43_1_1"/>
not <font color="Maroon">T</font> is <a href="abcmiz_0.html#V4" target="_self">void</a>
 ;<br/>

<b>thus </b><a NAME="E9:43_1_1"/>
<font color="Maroon">T</font> is <a href="abcmiz_0.html#V2" target="_self">Mizar-widening-like</a>
 ;<br/>

<a NAME="E10:43_1_1"/><i><font color="Green">E32</font></i>: 
( 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 &amp; <font color="Maroon">n</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> &amp; <font color="Maroon">n</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 
<b>by </b><i><a class="ref" href="funct_4.html#T66">FUNCT_4:66</a></i>;<br/>
<b>hence </b><a NAME="E11:43_1_1"/>
( <font color="Maroon">T</font> is <a href="abcmiz_0.html#V5" target="_self">involutive</a> &amp; <font color="Maroon">T</font> is <a href="abcmiz_0.html#V6" target="_self">without_fixpoints</a> )
 <b>by </b><i/>;<br/>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="abcmiz_0.html#D9" target="_self">ABCMIZ_0:def 9</a>
<div class="add"><b>let </b><font color="Maroon">t</font> be   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="abcmiz_0.html#NM2">adjective</a> of <font color="Maroon">T</font>;<br/><a NAME="E1:43_1_1_1"/><i><font color="Green">E35</font></i>: 
( ( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 1 ) &amp;  <a href="abcmiz_0.html#K1" target="_self">non-</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E2:43_1_1_1"/>
 <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/><b>hence </b><a NAME="E3:43_1_1_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">t</font> implies  not  <a href="abcmiz_0.html#K1" target="_self">non-</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">t</font> )
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="abcmiz_0.html#D11" target="_self">ABCMIZ_0:def 11</a>
<div class="add"><b>let </b><font color="Maroon">t1</font> be   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font>, <font color="Maroon">t2</font> be   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font>;<br/><a NAME="E1:43_1_1_2"/>
(  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">t2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> &amp;  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">t1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> &amp;  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">t2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> )
 <b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/><b>hence </b><a NAME="E2:43_1_1_2"/>
 <a href="abcmiz_0.html#K2" target="_self">adjs</a> <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">t2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">t1</font></span>)</span> <a href="finsub_1.html#K3">/\</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">t2</font></span>)</span>
 ;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">a</font> be   <a href="abcmiz_0.html#NM2">adjective</a> of <font color="Maroon">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="abcmiz_0.html#D14" target="_self">ABCMIZ_0:def 14</a><br/>

<a NAME="E14:43_1_1"/><i><font color="Green">E43</font></i>: 
( ( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 1 ) &amp;  <a href="abcmiz_0.html#K1" target="_self">non-</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon">t</font> being   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font>;<br/>
<a NAME="E16:43_1_1"/>
 <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<a NAME="E17:43_1_1"/><b>then </b>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">t</font> or  <a href="abcmiz_0.html#K1" target="_self">non-</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">t</font> )
 
<b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E18:43_1_1"/><b>then </b>
( <font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K3" target="_self">types</a> <font color="Maroon">a</font> or <font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K3" target="_self">types</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K1" target="_self">non-</a> <font color="Maroon">a</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E19:43_1_1"/>
not <span class="p1">(<span class="default"><a href="abcmiz_0.html#K3" target="_self">types</a> <font color="Maroon">a</font></span>)</span> <a href="finsub_1.html#K1">\/</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K3" target="_self">types</a> <span class="p2">(<span class="default"><a href="abcmiz_0.html#K1" target="_self">non-</a> <font color="Maroon">a</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


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