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<span class="kw">set </span><font color="Maroon" title="c1">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">set </span><font color="Maroon" title="c2">A</font> =  the   non  <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a>   <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>   <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>   <a href="abcmiz_0.html#L1" title="ABCMIZ_0:struct.1">AdjectiveStr</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">f</font> =  the   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  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">(<span class="default"><a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a>  the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of  the   non  <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a>   <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>   <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>   <a href="abcmiz_0.html#L1" title="ABCMIZ_0:struct.1">AdjectiveStr</a> </span>)</span>;<br/>
<span class="kw">take </span><font color="Maroon" title="c4">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> , the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of  the   non  <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a>   <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>   <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>   <a href="abcmiz_0.html#L1" title="ABCMIZ_0:struct.1">AdjectiveStr</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> , the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</a> of  the   non  <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a>   <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>   <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>   <a href="abcmiz_0.html#L1" title="ABCMIZ_0:struct.1">AdjectiveStr</a> , the   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  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">(<span class="default"><a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a>  the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of  the   non  <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a>   <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>   <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>   <a href="abcmiz_0.html#L1" title="ABCMIZ_0:struct.1">AdjectiveStr</a> </span>)</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="c4">T</font> is 1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>  &amp; <font color="Maroon" title="c4">T</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>  &amp;  not <font color="Maroon" title="c4">T</font> is  <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a>  &amp; <font color="Maroon" title="c4">T</font> is  <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>  &amp; <font color="Maroon" title="c4">T</font> is  <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>  &amp; <font color="Maroon" title="c4">T</font> is  <a href="abcmiz_0.html#V7" title="ABCMIZ_0:attr.7">strict</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E1:24_1_1"/>
<font color="Maroon" title="c4">T</font> is 1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</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></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="c4">T</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>  &amp;  not <font color="Maroon" title="c4">T</font> is  <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a>  &amp; <font color="Maroon" title="c4">T</font> is  <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>  &amp; <font color="Maroon" title="c4">T</font> is  <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>  &amp; <font color="Maroon" title="c4">T</font> is  <a href="abcmiz_0.html#V7" title="ABCMIZ_0:attr.7">strict</a>  )</span><br/>

<a NAME="E2:24_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  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>  #) <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 <font color="Maroon" title="c4">T</font>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">T</font> #)
 
;<br/>
<span class="kw">hence </span><a NAME="E3:24_1_1"/>
<font color="Maroon" title="c4">T</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_8.html#T12" onmouseover="rs('waybel_8/T12')" onmouseout="rh()">WAYBEL_8:12</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"> (  not <font color="Maroon" title="c4">T</font> is  <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a>  &amp; <font color="Maroon" title="c4">T</font> is  <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>  &amp; <font color="Maroon" title="c4">T</font> is  <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>  &amp; <font color="Maroon" title="c4">T</font> is  <a href="abcmiz_0.html#V7" title="ABCMIZ_0:attr.7">strict</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E4:24_1_1"/>
 not <font color="Maroon" title="c4">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="c4">T</font> is  <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>  &amp; <font color="Maroon" title="c4">T</font> is  <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>  &amp; <font color="Maroon" title="c4">T</font> is  <a href="abcmiz_0.html#V7" title="ABCMIZ_0:attr.7">strict</a>  )</span><br/>

<a NAME="E5:24_1_1"/>
 <a href="abcmiz_0.html#G1" title="ABCMIZ_0:aggr.1">AdjectiveStr</a>(#  the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of  the   non  <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a>   <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>   <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>   <a href="abcmiz_0.html#L1" title="ABCMIZ_0:struct.1">AdjectiveStr</a> , the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</a> of  the   non  <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a>   <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>   <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>   <a href="abcmiz_0.html#L1" title="ABCMIZ_0:struct.1">AdjectiveStr</a>  #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#G1" title="ABCMIZ_0:aggr.1">AdjectiveStr</a>(#  the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c4">T</font>, the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</a> of <font color="Maroon" title="c4">T</font> #)
 
;<br/>
<span class="kw">hence </span><a NAME="E6:24_1_1"/>
( <font color="Maroon" title="c4">T</font> is  <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>  &amp; <font color="Maroon" title="c4">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="ref" href="abcmiz_0.html#T5" target="_self" onmouseover="rs('abcmiz_0/T5')" onmouseout="rh()">Th5</a>, <a class="ref" href="abcmiz_0.html#T6" target="_self" onmouseover="rs('abcmiz_0/T6')" onmouseout="rh()">Th6</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="c4">T</font> is  <a href="abcmiz_0.html#V7" title="ABCMIZ_0:attr.7">strict</a> </span><br/>

<span class="kw">thus </span><a NAME="E7:24_1_1"/>
<font color="Maroon" title="c4">T</font> is  <a href="abcmiz_0.html#V7" title="ABCMIZ_0:attr.7">strict</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/>


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