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

<span class="kw">set </span><font color="Maroon" title="c1">P</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c2">T</font> =  <a href="abcmiz_0.html#G3" title="ABCMIZ_0:aggr.3">TAS-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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> , the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> , the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> , the <a href="abcmiz_0.html#U3" title="ABCMIZ_0:sel.3">adj-map</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> ,<span class="p1">(<span class="default"><a href="abcmiz_0.html#K9" title="ABCMIZ_0:func.9">sub</a>  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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> </span>)</span> #);<br/>
<a NAME="E1:107_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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</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 <a href="abcmiz_0.html#G3" title="ABCMIZ_0:aggr.3">TAS-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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> , the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> , the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> , the <a href="abcmiz_0.html#U3" title="ABCMIZ_0:sel.3">adj-map</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> ,<span class="p1">(<span class="default"><a href="abcmiz_0.html#K9" title="ABCMIZ_0:func.9">sub</a>  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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> </span>)</span> #), the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <a href="abcmiz_0.html#G3" title="ABCMIZ_0:aggr.3">TAS-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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> , the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> , the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> , the <a href="abcmiz_0.html#U3" title="ABCMIZ_0:sel.3">adj-map</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> ,<span class="p1">(<span class="default"><a href="abcmiz_0.html#K9" title="ABCMIZ_0:func.9">sub</a>  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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> </span>)</span> #) #)
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">T</font> =  <a href="abcmiz_0.html#G3" title="ABCMIZ_0:aggr.3">TAS-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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> , the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> , the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> , the <a href="abcmiz_0.html#U3" title="ABCMIZ_0:sel.3">adj-map</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> ,<span class="p1">(<span class="default"><a href="abcmiz_0.html#K9" title="ABCMIZ_0:func.9">sub</a>  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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> </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>   non  <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a>   <a href="abcmiz_0.html#V11" title="ABCMIZ_0:attr.11">strict</a>   <a href="abcmiz_0.html#L3" title="ABCMIZ_0:struct.3">TAS-structure</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#D4" target="_self" onmouseover="rs('abcmiz_0/D4')" onmouseout="rh()">Def4</a>, <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="c3">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="c3">T</font> is  <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V12" title="ABCMIZ_0:attr.12">non-absorbing</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V13" title="ABCMIZ_0:attr.13">subjected</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V14" title="ABCMIZ_0:attr.14">commutative</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E3:107_1_1"/>
<font color="Maroon" title="c3">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="c3">T</font> is  <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V12" title="ABCMIZ_0:attr.12">non-absorbing</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V13" title="ABCMIZ_0:attr.13">subjected</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V14" title="ABCMIZ_0:attr.14">commutative</a>  )</span><br/>

<a NAME="E4:107_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  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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> , the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</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="c3">T</font>, the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</a> of <font color="Maroon" title="c3">T</font> #)
 
;<br/>
<span class="kw">hence </span><a NAME="E5:107_1_1"/>
( <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V5" title="ABCMIZ_0:attr.5">involutive</a>  &amp; <font color="Maroon" title="c3">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="c3">T</font> is  <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V12" title="ABCMIZ_0:attr.12">non-absorbing</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V13" title="ABCMIZ_0:attr.13">subjected</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V14" title="ABCMIZ_0:attr.14">commutative</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E6:107_1_1"/>
( <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#T8" target="_self" onmouseover="rs('abcmiz_0/T8')" onmouseout="rh()">Th8</a>, <a class="ref" href="abcmiz_0.html#T9" target="_self" onmouseover="rs('abcmiz_0/T9')" onmouseout="rh()">Th9</a>, <a class="ref" href="abcmiz_0.html#T17" target="_self" onmouseover="rs('abcmiz_0/T17')" onmouseout="rh()">Th17</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="c3">T</font> is  <a href="abcmiz_0.html#V12" title="ABCMIZ_0:attr.12">non-absorbing</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V13" title="ABCMIZ_0:attr.13">subjected</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V14" title="ABCMIZ_0:attr.14">commutative</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#D26" target="_self" onmouseover="rs('abcmiz_0/D26')" onmouseout="rh()">ABCMIZ_0:def 26</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="c3">T</font> is  <a href="abcmiz_0.html#V13" title="ABCMIZ_0:attr.13">subjected</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V14" title="ABCMIZ_0:attr.14">commutative</a>  )</span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c4">a</font> be   <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c3">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#K10" title="ABCMIZ_0:func.10">sub</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#K10" title="ABCMIZ_0:func.10">sub</a> <font color="Maroon" title="c4">a</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c5">b</font> = <font color="Maroon" title="c4">a</font> as   <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a>  ;<br/><span class="kw">thus </span> <a href="abcmiz_0.html#K10" title="ABCMIZ_0:func.10">sub</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c4">a</font></span>)</span> = 
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <span class="p3">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p2">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <span class="p3">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <span class="p4">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#D22" target="_self" onmouseover="rs('abcmiz_0/D22')" onmouseout="rh()">Def22</a></span>
<br/>.= 
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <span class="p3">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p2">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#D6" target="_self" onmouseover="rs('abcmiz_0/D6')" onmouseout="rh()">Def6</a></span>
<br/>.= 
 <a href="abcmiz_0.html#K10" title="ABCMIZ_0:func.10">sub</a> <font color="Maroon" title="c4">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#D22" target="_self" onmouseover="rs('abcmiz_0/D22')" onmouseout="rh()">Def22</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>

<a NAME="E8:107_1_1"/><span class="lab"><font color="Green" title="E58">A1</font></span>: 
 <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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</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="c3">T</font>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">T</font> #)
 
;<br/>
<span class="kw">thus </span><a NAME="E9:107_1_1"/>
<font color="Maroon" title="c3">T</font> is  <a href="abcmiz_0.html#V13" title="ABCMIZ_0:attr.13">subjected</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="c3">T</font> is  <a href="abcmiz_0.html#V14" title="ABCMIZ_0:attr.14">commutative</a> </span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="107_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">a</font> be   <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c3">T</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="abcmiz_0.html#D25" target="_self" onmouseover="rs('abcmiz_0/D25')" onmouseout="rh()">ABCMIZ_0:def 25</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"> ( <span class="p1">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c4">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="c4">a</font></span>)</span></span>)</span> <a href="lattice3.html#R2" title="LATTICE3:pred.2">is_&lt;=_than</a>  <a href="abcmiz_0.html#K10" title="ABCMIZ_0:func.10">sub</a> <font color="Maroon" title="c4">a</font> &amp; (  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <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="c4">a</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="abcmiz_0.html#K10" title="ABCMIZ_0:func.10">sub</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p2">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <span class="p3">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c4">a</font></span>)</span></span>)</span></span>)</span> ) )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">b</font> = <font color="Maroon" title="c4">a</font> as   <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="abcmiz_0.html#V2" title="ABCMIZ_0:attr.2">Mizar-widening-like</a>   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#V7" title="ABCMIZ_0:attr.7">strict</a>   <a href="abcmiz_0.html#V8" title="ABCMIZ_0:attr.8">consistent</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#V10" title="ABCMIZ_0:attr.10">adjs-typed</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a>  ;<br/>
<a NAME="E2:107_1_1_2"/><span class="lab"><font color="Green" title="E59">A2</font></span>: 
 <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="c4">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c5">b</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#T11" target="_self" onmouseover="rs('abcmiz_0/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<a NAME="E3:107_1_1_2"/>
 <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c5">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#T11" target="_self" onmouseover="rs('abcmiz_0/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<a NAME="E4:107_1_1_2"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p2">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <span class="p3">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c4">a</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p2">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <span class="p3">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:107_1_1"><span class="lab"><font color="Green" title="E58">A1</font></span></a>, <a class="txt" href="#E2:107_1_1_2"><span class="lab"><font color="Green" title="E59">A2</font></span></a>, <a class="ref" href="yellow_0.html#T17" onmouseover="rs('yellow_0/T17')" onmouseout="rh()">YELLOW_0:17</a>, <a class="ref" href="yellow_0.html#T26" onmouseover="rs('yellow_0/T26')" onmouseout="rh()">YELLOW_0:26</a></span>;<br/>
<a NAME="E5:107_1_1_2"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p2">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <span class="p3">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c4">a</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#K10" title="ABCMIZ_0:func.10">sub</a> <font color="Maroon" title="c4">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#D22" target="_self" onmouseover="rs('abcmiz_0/D22')" onmouseout="rh()">Def22</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:107_1_1_2"/>
( <span class="p1">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c4">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="c4">a</font></span>)</span></span>)</span> <a href="lattice3.html#R2" title="LATTICE3:pred.2">is_&lt;=_than</a>  <a href="abcmiz_0.html#K10" title="ABCMIZ_0:func.10">sub</a> <font color="Maroon" title="c4">a</font> &amp; (  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <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="c4">a</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="abcmiz_0.html#K10" title="ABCMIZ_0:func.10">sub</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p2">(<span class="default"><a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <span class="p3">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c4">a</font></span>)</span></span>)</span></span>)</span> ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T32" onmouseover="rs('yellow_0/T32')" onmouseout="rh()">YELLOW_0:32</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="c4">t1</font>, <font color="Maroon" title="c5">t2</font> be   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c3">T</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="abcmiz_0.html#D30" target="_self" onmouseover="rs('abcmiz_0/D30')" onmouseout="rh()">ABCMIZ_0:def 30</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">  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="c3">T</font>  st <font color="Olive" title="b1">a</font> <a href="abcmiz_0.html#R4" title="ABCMIZ_0:pred.4">is_properly_applicable_to</a> <font color="Maroon" title="c4">t1</font> &amp; <font color="Olive" title="b1">a</font> <a href="abcmiz_0.html#K5" title="ABCMIZ_0:func.5">ast</a> <font color="Maroon" title="c4">t1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">t2</font> holds <br/> ex <font color="Olive" title="b2">A</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of  the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c3">T</font> st <br/>( <font color="Olive" title="b2">A</font> <a href="abcmiz_0.html#R6" title="ABCMIZ_0:pred.6">is_properly_applicable_to</a> <font color="Maroon" title="c4">t1</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c5">t2</font> &amp; <font color="Olive" title="b2">A</font> <a href="abcmiz_0.html#K6" title="ABCMIZ_0:func.6">ast</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">t1</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c5">t2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">t2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">a</font> be   <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c3">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="c6">a</font> <a href="abcmiz_0.html#R4" title="ABCMIZ_0:pred.4">is_properly_applicable_to</a> <font color="Maroon" title="c4">t1</font> &amp; <font color="Maroon" title="c6">a</font> <a href="abcmiz_0.html#K5" title="ABCMIZ_0:func.5">ast</a> <font color="Maroon" title="c4">t1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">t2</font> implies  ex <font color="Olive" title="b1">A</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of  the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c3">T</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="abcmiz_0.html#R6" title="ABCMIZ_0:pred.6">is_properly_applicable_to</a> <font color="Maroon" title="c4">t1</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c5">t2</font> &amp; <font color="Olive" title="b1">A</font> <a href="abcmiz_0.html#K6" title="ABCMIZ_0:func.6">ast</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">t1</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c5">t2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">t2</font> ) )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E10:107_1_1"/>
<font color="Maroon" title="c6">a</font> <a href="abcmiz_0.html#R4" title="ABCMIZ_0:pred.4">is_properly_applicable_to</a> <font color="Maroon" title="c4">t1</font>
 <span class="kw">and </span><br/><a NAME="E11:107_1_1"/>
<font color="Maroon" title="c6">a</font> <a href="abcmiz_0.html#K5" title="ABCMIZ_0:func.5">ast</a> <font color="Maroon" title="c4">t1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">t2</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">  ex <font color="Olive" title="b1">A</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of  the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c3">T</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="abcmiz_0.html#R6" title="ABCMIZ_0:pred.6">is_properly_applicable_to</a> <font color="Maroon" title="c4">t1</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c5">t2</font> &amp; <font color="Olive" title="b1">A</font> <a href="abcmiz_0.html#K6" title="ABCMIZ_0:func.6">ast</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">t1</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c5">t2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">t2</font> )</span><br/>

<span class="kw">take </span><font color="Maroon" title="c7">A</font> =  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a>  the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c3">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="c7">A</font> <a href="abcmiz_0.html#R6" title="ABCMIZ_0:pred.6">is_properly_applicable_to</a> <font color="Maroon" title="c4">t1</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c5">t2</font> &amp; <font color="Maroon" title="c7">A</font> <a href="abcmiz_0.html#K6" title="ABCMIZ_0:func.6">ast</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">t1</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c5">t2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">t2</font> )</span><br/>

<span class="kw">thus </span><a NAME="E12:107_1_1"/>
<font color="Maroon" title="c7">A</font> <a href="abcmiz_0.html#R6" title="ABCMIZ_0:pred.6">is_properly_applicable_to</a> <font color="Maroon" title="c4">t1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c5">t2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#T63" target="_self" onmouseover="rs('abcmiz_0/T63')" onmouseout="rh()">Th63</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="c7">A</font> <a href="abcmiz_0.html#K6" title="ABCMIZ_0:func.6">ast</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">t1</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c5">t2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">t2</font></span><br/>

<span class="kw">thus </span><a NAME="E13:107_1_1"/>
<font color="Maroon" title="c7">A</font> <a href="abcmiz_0.html#K6" title="ABCMIZ_0:func.6">ast</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">t1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c5">t2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">t2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" onmouseover="rs('struct_0/D10')" onmouseout="rh()">STRUCT_0:def 10</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>
