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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a> <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a> <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a> <a href="abcmiz_0.html#V1" title="ABCMIZ_0:attr.1">Noetherian</a> non <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a> <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a> <a href="abcmiz_0.html#V14" title="ABCMIZ_0:attr.14">commutative</a>  <a href="abcmiz_0.html#L3" title="ABCMIZ_0:struct.3">TAS-structure</a> ;<br/><b>let </b><font color="Maroon" title="c2">t1</font>, <font color="Maroon" title="c3">t2</font> be   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c1">T</font>;<br/><b>let </b><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="c1">T</font>;<br/>





<b>set </b><font color="Maroon" title="c5">R</font> = <font color="Maroon" title="c1">T</font> <a href="abcmiz_0.html#K11" title="ABCMIZ_0:func.11">@--&gt;</a> ;<br/>
<a NAME="E1:132"/><i><font color="Green" title="E85">A1</font></i>: 
<font color="Maroon" title="c1">T</font> <a href="abcmiz_0.html#K11" title="ABCMIZ_0:func.11">@--&gt;</a>  is  <a href="rewrite1.html#V3" title="REWRITE1:attr.3">strongly-normalizing</a> <a href="rewrite1.html#V4" title="REWRITE1:attr.4">with_UN_property</a> <a href="rewrite1.html#V8" title="REWRITE1:attr.8">with_Church-Rosser_property</a> <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>
 
<b>by </b><i><a class="ref" href="abcmiz_0.html#T70" target="_self" title="ABCMIZ_0:th.70">Th70</a>, <a class="ref" href="abcmiz_0.html#T78" target="_self" title="ABCMIZ_0:th.78">Th78</a></i>;<br/>
<b>set </b><font color="Maroon" title="c6">AA</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">t'</font> where <font color="Olive" title="b1">t'</font> is   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c1">T</font> :  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="c1">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="Olive" title="b1">t'</font> &amp; <font color="Olive" title="b2">A</font> <a href="abcmiz_0.html#K6" title="ABCMIZ_0:func.6">ast</a> <font color="Olive" title="b1">t'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t2</font> ) </span>}</span> ;<br/>
<b>assume </b><a NAME="E2:132"/>
( <font color="Maroon" title="c4">a</font> <a href="abcmiz_0.html#R4" title="ABCMIZ_0:pred.4">is_properly_applicable_to</a> <font color="Maroon" title="c2">t1</font> &amp; <font color="Maroon" title="c4">a</font> <a href="abcmiz_0.html#K5" title="ABCMIZ_0:func.5">ast</a> <font color="Maroon" title="c2">t1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font> )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c7">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="c1">T</font><b> such that </b><br/><a NAME="E4:132"/><i><font color="Green" title="E86">A2</font></i>: 
( <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="c2">t1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font></span>)</span> &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="c2">t1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p2">(<span class="default"><a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font> )
 <b>by </b><i><a class="ref" href="abcmiz_0.html#D30" target="_self" title="ABCMIZ_0:def.30">Def30</a></i>;<br/>
<a NAME="E5:132"/>
 <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> <font color="Maroon" title="c3">t2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="abcmiz_0.html#K11" title="ABCMIZ_0:func.11">@--&gt;</a> </span>)</span> <a href="rewrite1.html#R4" title="REWRITE1:pred.4">is_a_normal_form_of</a> <font color="Maroon" title="c3">t2</font>,<font color="Maroon" title="c1">T</font> <a href="abcmiz_0.html#K11" title="ABCMIZ_0:func.11">@--&gt;</a> 
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E1:132"><i><font color="Green" title="E85">A1</font></i></a>, <a class="ref" href="rewrite1.html#T55" title="REWRITE1:th.55">REWRITE1:55</a></i>;<br/>
<a NAME="E6:132"/><b>then </b>
<font color="Maroon" title="c1">T</font> <a href="abcmiz_0.html#K11" title="ABCMIZ_0:func.11">@--&gt;</a>  <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c3">t2</font>, <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> <font color="Maroon" title="c3">t2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="abcmiz_0.html#K11" title="ABCMIZ_0:func.11">@--&gt;</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="rewrite1.html#D6" title="REWRITE1:def.6">REWRITE1:def 6</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c8">B</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="c1">T</font><b> such that </b><br/><a NAME="E8:132"/><i><font color="Green" title="E87">A3</font></i>: 
( <font color="Maroon" title="c8">B</font> <a href="abcmiz_0.html#R6" title="ABCMIZ_0:pred.6">is_properly_applicable_to</a>  <a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font> &amp; <font color="Maroon" title="c3">t2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">B</font> <a href="abcmiz_0.html#K6" title="ABCMIZ_0:func.6">ast</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font></span>)</span> )
 <b>by </b><i><a class="ref" href="abcmiz_0.html#T77" target="_self" title="ABCMIZ_0:th.77">Th77</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">v1</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E10:132"/><i><font color="Green" title="E88">A4</font></i>: 
(  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c9">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">A</font> &amp; <font color="Maroon" title="c9">v1</font> <a href="abcmiz_0.html#R5" title="ABCMIZ_0:pred.5">is_properly_applicable_to</a> <font color="Maroon" title="c2">t1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font></span>)</span> )
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E4:132"><i><font color="Green" title="E86">A2</font></i></a>, <a class="ref" href="abcmiz_0.html#D29" target="_self" title="ABCMIZ_0:def.29">Def29</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">v2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E12:132"/><i><font color="Green" title="E89">A5</font></i>: 
(  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c10">v2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">B</font> &amp; <font color="Maroon" title="c10">v2</font> <a href="abcmiz_0.html#R5" title="ABCMIZ_0:pred.5">is_properly_applicable_to</a>  <a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font> )
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E8:132"><i><font color="Green" title="E87">A3</font></i></a>, <a class="ref" href="abcmiz_0.html#D29" target="_self" title="ABCMIZ_0:def.29">Def29</a></i>;<br/>
<a NAME="E13:132"/><i><font color="Green" title="E90">A6</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">v1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c10">v2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">A</font> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c8">B</font>
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E10:132"><i><font color="Green" title="E88">A4</font></i></a>, <a class="txt" href="abcmiz_0.html#E12:132"><i><font color="Green" title="E89">A5</font></i></a>, <a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></i>;<br/>
<a NAME="E14:132"/><i><font color="Green" title="E91">A7</font></i>: 
( <font color="Maroon" title="c9">v1</font> <a href="abcmiz_0.html#R3" title="ABCMIZ_0:pred.3">is_applicable_to</a> <font color="Maroon" title="c2">t1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font></span>)</span> &amp; <font color="Maroon" title="c10">v2</font> <a href="abcmiz_0.html#R3" title="ABCMIZ_0:pred.3">is_applicable_to</a>  <a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font> )
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E10:132"><i><font color="Green" title="E88">A4</font></i></a>, <a class="txt" href="abcmiz_0.html#E12:132"><i><font color="Green" title="E89">A5</font></i></a>, <a class="ref" href="abcmiz_0.html#T58" target="_self" title="ABCMIZ_0:th.58">Th58</a></i>;<br/>
<a NAME="E15:132"/><b>then </b><i><font color="Green" title="E92">A8</font></i>: 
 <a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">v1</font> <a href="abcmiz_0.html#K8" title="ABCMIZ_0:func.8">ast</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">t1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p2">(<span class="default"><a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E4:132"><i><font color="Green" title="E86">A2</font></i></a>, <a class="txt" href="abcmiz_0.html#E10:132"><i><font color="Green" title="E88">A4</font></i></a>, <a class="ref" href="abcmiz_0.html#T57" target="_self" title="ABCMIZ_0:th.57">Th57</a></i>;<br/>
<a NAME="E16:132"/><b>then </b>
<font color="Maroon" title="c9">v1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c10">v2</font> <a href="abcmiz_0.html#R5" title="ABCMIZ_0:pred.5">is_properly_applicable_to</a> <font color="Maroon" title="c2">t1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E10:132"><i><font color="Green" title="E88">A4</font></i></a>, <a class="txt" href="abcmiz_0.html#E12:132"><i><font color="Green" title="E89">A5</font></i></a>, <a class="ref" href="abcmiz_0.html#T62" target="_self" title="ABCMIZ_0:th.62">Th62</a></i>;<br/>
<a NAME="E17:132"/><b>then </b><i><font color="Green" title="E93">A9</font></i>: 
( <font color="Maroon" title="c7">A</font> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c8">B</font> <a href="abcmiz_0.html#R6" title="ABCMIZ_0:pred.6">is_properly_applicable_to</a> <font color="Maroon" title="c2">t1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font></span>)</span> &amp; <font color="Maroon" title="c9">v1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c10">v2</font> <a href="abcmiz_0.html#R3" title="ABCMIZ_0:pred.3">is_applicable_to</a> <font color="Maroon" title="c2">t1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E13:132"><i><font color="Green" title="E90">A6</font></i></a>, <a class="ref" href="abcmiz_0.html#D29" target="_self" title="ABCMIZ_0:def.29">Def29</a>, <a class="ref" href="abcmiz_0.html#T58" target="_self" title="ABCMIZ_0:th.58">Th58</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><font color="Maroon" title="c7">A</font> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c8">B</font></span>)</span> <a href="abcmiz_0.html#K6" title="ABCMIZ_0:func.6">ast</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">t1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p2">(<span class="default"><a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">v1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c10">v2</font></span>)</span> <a href="abcmiz_0.html#K8" title="ABCMIZ_0:func.8">ast</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">t1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p2">(<span class="default"><a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="abcmiz_0.html#E13:132"><i><font color="Green" title="E90">A6</font></i></a>, <a class="ref" href="abcmiz_0.html#T57" target="_self" title="ABCMIZ_0:th.57">Th57</a></i>
<br/>.= 
<font color="Maroon" title="c10">v2</font> <a href="abcmiz_0.html#K8" title="ABCMIZ_0:func.8">ast</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font></span>)</span>
<b>by </b><i><a class="txt" href="abcmiz_0.html#E15:132"><i><font color="Green" title="E92">A8</font></i></a>, <a class="ref" href="abcmiz_0.html#T38" target="_self" title="ABCMIZ_0:th.38">Th38</a></i>
<br/>.= 
<font color="Maroon" title="c3">t2</font>
<b>by </b><i><a class="txt" href="abcmiz_0.html#E8:132"><i><font color="Green" title="E87">A3</font></i></a>, <a class="txt" href="abcmiz_0.html#E12:132"><i><font color="Green" title="E89">A5</font></i></a>, <a class="txt" href="abcmiz_0.html#E14:132"><i><font color="Green" title="E91">A7</font></i></a>, <a class="ref" href="abcmiz_0.html#T57" target="_self" title="ABCMIZ_0:th.57">Th57</a></i>
;<br/>
<a NAME="E19:132"/><b>then </b>
( <font color="Maroon" title="c2">t1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">t'</font> where <font color="Olive" title="b1">t'</font> is   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c1">T</font> :  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="c1">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="Olive" title="b1">t'</font> &amp; <font color="Olive" title="b2">A</font> <a href="abcmiz_0.html#K6" title="ABCMIZ_0:func.6">ast</a> <font color="Olive" title="b1">t'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t2</font> ) </span>}</span>  &amp;  <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">t'</font> where <font color="Olive" title="b1">t'</font> is   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c1">T</font> :  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="c1">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="Olive" title="b1">t'</font> &amp; <font color="Olive" title="b2">A</font> <a href="abcmiz_0.html#K6" title="ABCMIZ_0:func.6">ast</a> <font color="Olive" title="b1">t'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t2</font> ) </span>}</span> ,<font color="Maroon" title="c1">T</font> )
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E17:132"><i><font color="Green" title="E93">A9</font></i></a>, <a class="ref" href="abcmiz_0.html#T81" target="_self" title="ABCMIZ_0:th.81">Th81</a></i>;<br/>
<a NAME="E20:132"/><b>then </b>
<font color="Maroon" title="c2">t1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font></span>)</span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">t'</font> where <font color="Olive" title="b1">t'</font> is   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c1">T</font> :  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="c1">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="Olive" title="b1">t'</font> &amp; <font color="Olive" title="b2">A</font> <a href="abcmiz_0.html#K6" title="ABCMIZ_0:func.6">ast</a> <font color="Olive" title="b1">t'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t2</font> ) </span>}</span> ,<font color="Maroon" title="c1">T</font>
 
<b>by </b><i><a class="ref" href="yellow_4.html#T1" title="YELLOW_4:th.1">YELLOW_4:1</a></i>;<br/>
<a NAME="E21:132"/><b>then </b>
( <font color="Maroon" title="c2">t1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font></span>)</span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font> &amp; <font color="Maroon" title="c2">t1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font></span>)</span> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c2">t1</font> )
 
<b>by </b><i><a class="ref" href="abcmiz_0.html#T81" target="_self" title="ABCMIZ_0:th.81">Th81</a>, <a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</a></i>;<br/>
<b>hence </b><a NAME="E22:132"/>
<font color="Maroon" title="c2">t1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c3">t2</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#D2" title="YELLOW_0:def.2">YELLOW_0:def 2</a></i>;<br/>


</div>
