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<span class="kw">consider </span><font color="Maroon" title="c1">R</font> being  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</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="c2">A</font> being  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> , <font color="Maroon" title="c3">f</font> being   <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 <font color="Maroon" title="c1">R</font>,<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 <font color="Maroon" title="c2">A</font></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 <font color="Maroon" title="c1">R</font>,the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c2">A</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font>,the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">f</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="c4">T</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</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="struct_0.html#V2" title="STRUCT_0:attr.2">empty</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="E2:25_1_1"/>
<font color="Maroon" title="c4">T</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> 
 ; <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="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="struct_0.html#V2" title="STRUCT_0:attr.2">empty</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="E3:25_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 <font color="Maroon" title="c1">R</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font> #) <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="E4:25_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" title="WAYBEL_8:th.12">WAYBEL_8:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c4">T</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</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="E5:25_1_1"/>
( not <font color="Maroon" title="c4">T</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp; 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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="E6:25_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 <font color="Maroon" title="c2">A</font>,the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</a> of <font color="Maroon" title="c2">A</font> #) <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="E7:25_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" title="ABCMIZ_0:th.5">Th5</a>, <a class="ref" href="abcmiz_0.html#T6" target="_self" title="ABCMIZ_0:th.6">Th6</a></span>; <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="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="E8:25_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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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