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<span class="kw">let </span><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> ; <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">t1</font>, <font color="Olive" title="b2">t2</font> being   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c1">T</font><br/>  for <font color="Olive" title="b3">a</font> being   <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b3">a</font> <a href="abcmiz_0.html#R4" title="ABCMIZ_0:pred.4">is_properly_applicable_to</a> <font color="Olive" title="b1">t1</font> &amp; <font color="Olive" title="b3">a</font> <a href="abcmiz_0.html#K5" title="ABCMIZ_0:func.5">ast</a> <font color="Olive" title="b1">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="Olive" title="b2">t2</font> holds <br/><font color="Olive" title="b1">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="Olive" title="b2">t2</font></span><br/><span class="kw">let </span><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>; <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="c1">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="c2">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="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> holds <br/><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></span><br/><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="c1">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="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> implies <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> )</span><br/>





<span class="kw">set </span><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/>
<span class="kw">set </span><font color="Maroon" title="c6">AA</font> = <span class="p1"> { <span class="default"> <font color="Olive" title="b1">t9</font> where <font color="Olive" title="b1">t9</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">t9</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">t9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t2</font> ) </span> } </span> ;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:126"/><span class="lab"><font color="Green" title="E75">A1</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E2:126"/><span class="lab"><font color="Green" title="E76">A2</font></span>: 
<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>
 ; <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="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></span><br/>

<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E4:126"/><span class="lab"><font color="Green" title="E77">A3</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E5:126"/><span class="lab"><font color="Green" title="E78">A4</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:126"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="txt" href="#E2:126"><span class="lab"><font color="Green" title="E76">A2</font></span></a>, <a class="ref" href="abcmiz_0.html#D30" target="_self" onmouseover="rs('abcmiz_0/D30')" onmouseout="rh()">Def30</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c8">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><span class="kw"> such that </span><br/><a NAME="E7:126"/><span class="lab"><font color="Green" title="E79">A5</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c8">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">A</font>
 <span class="kw">and </span><br/><a NAME="E8:126"/><span class="lab"><font color="Green" title="E80">A6</font></span>: 
<font color="Maroon" title="c8">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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:126"><span class="lab"><font color="Green" title="E77">A3</font></span></a></span>;<br/>
<a NAME="E9:126"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#T69" target="_self" onmouseover="rs('abcmiz_0/T69')" onmouseout="rh()">Th69</a>, <a class="ref" href="abcmiz_0.html#T77" target="_self" onmouseover="rs('abcmiz_0/T77')" onmouseout="rh()">Th77</a></span>;<br/>
<a NAME="E10:126"/><span class="kw">then </span>
 <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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite1.html#T54" onmouseover="rs('rewrite1/T54')" onmouseout="rh()">REWRITE1:54</a></span>;<br/>
<a NAME="E11:126"/><span class="kw">then </span>
<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>)
 
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">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><span class="kw"> such that </span><br/><a NAME="E13:126"/><span class="lab"><font color="Green" title="E81">A7</font></span>: 
<font color="Maroon" title="c9">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>
 <span class="kw">and </span><br/><a NAME="E14:126"/><span class="lab"><font color="Green" title="E82">A8</font></span>: 
<font color="Maroon" title="c3">t2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#T76" target="_self" onmouseover="rs('abcmiz_0/T76')" onmouseout="rh()">Th76</a></span>;<br/>
<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E16:126"/><span class="lab"><font color="Green" title="E83">A9</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c10">v2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">B</font>
 <span class="kw">and </span><br/><a NAME="E17:126"/><span class="lab"><font color="Green" title="E84">A10</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:126"><span class="lab"><font color="Green" title="E81">A7</font></span></a></span>;<br/>
<a NAME="E18:126"/><span class="lab"><font color="Green" title="E85">A11</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">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="c9">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:126"><span class="lab"><font color="Green" title="E79">A5</font></span></a>, <a class="txt" href="#E16:126"><span class="lab"><font color="Green" title="E83">A9</font></span></a>, <a class="ref" href="finseq_1.html#T31" onmouseover="rs('finseq_1/T31')" onmouseout="rh()">FINSEQ_1:31</a></span>;<br/>
<a NAME="E19:126"/><span class="lab"><font color="Green" title="E86">A12</font></span>: 
 <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="c8">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:126"><span class="lab"><font color="Green" title="E78">A4</font></span></a>, <a class="txt" href="#E7:126"><span class="lab"><font color="Green" title="E79">A5</font></span></a>, <a class="txt" href="#E8:126"><span class="lab"><font color="Green" title="E80">A6</font></span></a>, <a class="ref" href="abcmiz_0.html#T56" target="_self" onmouseover="rs('abcmiz_0/T56')" onmouseout="rh()">Th56</a>, <a class="ref" href="abcmiz_0.html#T57" target="_self" onmouseover="rs('abcmiz_0/T57')" onmouseout="rh()">Th57</a></span>;<br/>
<a NAME="E20:126"/><span class="kw">then </span><span class="lab"><font color="Green" title="E87">A13</font></span>: 
<font color="Maroon" title="c8">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:126"><span class="lab"><font color="Green" title="E80">A6</font></span></a>, <a class="txt" href="#E17:126"><span class="lab"><font color="Green" title="E84">A10</font></span></a>, <a class="ref" href="abcmiz_0.html#T61" target="_self" onmouseover="rs('abcmiz_0/T61')" onmouseout="rh()">Th61</a></span>;<br/>
<a NAME="E21:126"/><span class="kw">then </span><span class="lab"><font color="Green" title="E88">A14</font></span>: 
<font color="Maroon" title="c7">A</font> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c9">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:126"><span class="lab"><font color="Green" title="E85">A11</font></span></a></span>;<br/>
<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="c9">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="c8">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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:126"><span class="lab"><font color="Green" title="E85">A11</font></span></a>, <a class="txt" href="#E20:126"><span class="lab"><font color="Green" title="E87">A13</font></span></a>, <a class="ref" href="abcmiz_0.html#T56" target="_self" onmouseover="rs('abcmiz_0/T56')" onmouseout="rh()">Th56</a>, <a class="ref" href="abcmiz_0.html#T57" target="_self" onmouseover="rs('abcmiz_0/T57')" onmouseout="rh()">Th57</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:126"><span class="lab"><font color="Green" title="E86">A12</font></span></a>, <a class="ref" href="abcmiz_0.html#T37" target="_self" onmouseover="rs('abcmiz_0/T37')" onmouseout="rh()">Th37</a></span>
<br/>.= 
<font color="Maroon" title="c3">t2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:126"><span class="lab"><font color="Green" title="E82">A8</font></span></a>, <a class="txt" href="#E16:126"><span class="lab"><font color="Green" title="E83">A9</font></span></a>, <a class="txt" href="#E17:126"><span class="lab"><font color="Green" title="E84">A10</font></span></a>, <a class="ref" href="abcmiz_0.html#T56" target="_self" onmouseover="rs('abcmiz_0/T56')" onmouseout="rh()">Th56</a>, <a class="ref" href="abcmiz_0.html#T57" target="_self" onmouseover="rs('abcmiz_0/T57')" onmouseout="rh()">Th57</a></span>
;<br/>
<a NAME="E23:126"/><span class="kw">then </span>
<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="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">t9</font> where <font color="Olive" title="b1">t9</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">t9</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">t9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t2</font> ) </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:126"><span class="lab"><font color="Green" title="E88">A14</font></span></a></span>;<br/>
<a NAME="E24:126"/><span class="kw">then </span>
<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">t9</font> where <font color="Olive" title="b1">t9</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">t9</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">t9</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>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#T80" target="_self" onmouseover="rs('abcmiz_0/T80')" onmouseout="rh()">Th80</a>, <a class="ref" href="yellow_4.html#T1" onmouseover="rs('yellow_4/T1')" onmouseout="rh()">YELLOW_4:1</a></span>;<br/>
<a NAME="E25:126"/><span class="kw">then </span><span class="lab"><font color="Green" title="E89">A15</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#T80" target="_self" onmouseover="rs('abcmiz_0/T80')" onmouseout="rh()">Th80</a></span>;<br/>
<a NAME="E26:126"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T22" onmouseover="rs('yellow_0/T22')" onmouseout="rh()">YELLOW_0:22</a></span>;<br/>
<span class="kw">hence </span><a NAME="E27:126"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:126"><span class="lab"><font color="Green" title="E89">A15</font></span></a>, <a class="ref" href="yellow_0.html#D2" onmouseover="rs('yellow_0/D2')" onmouseout="rh()">YELLOW_0:def 2</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/>


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