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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V3">transitive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="lattice3.html#V1">with_suprema</a> <a href="abcmiz_0.html#V1" target="_self">Noetherian</a> non <a href="abcmiz_0.html#V4" target="_self">void</a> <a href="abcmiz_0.html#V9" target="_self">adj-structured</a>  <a href="abcmiz_0.html#L3" target="_self">TAS-structure</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="finset_1.html#V1">finite</a> <a href="subset_1.html#NM2">Subset</a> of the <a href="abcmiz_0.html#U1" target="_self">adjectives</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:120"/><i><font color="Green">E74</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of the <a href="abcmiz_0.html#U1" target="_self">adjectives</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="abcmiz_0.html#R6" target="_self">is_properly_applicable_to</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="abcmiz_0.html#K6" target="_self">ast</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="abcmiz_0.html#K6" target="_self">ast</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be  <a href="funct_1.html#V2">one-to-one</a>  <a href="finseq_1.html#M2">FinSequence</a> of the <a href="abcmiz_0.html#U1" target="_self">adjectives</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E2:120"/><i><font color="Green">E75</font></i>: 
(  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="abcmiz_0.html#R5" target="_self">is_properly_applicable_to</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E3:120"/><i><font color="Green">E76</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K7" target="_self">apply</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="abcmiz_0.html#D19" target="_self">Def19</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>5</sub></font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E4:120"/><i><font color="Green">E77</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<a NAME="E5:120"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>5</sub></font> is   <a href="nat_1.html#NM1">Nat</a> )
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a>, <a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E6:120"/><b>then </b><i><font color="Green">E78</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K7" target="_self">apply</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E3:120"><i><font color="Green">E76</font></i></a>, <a class="txt" href="abcmiz_0.html#E4:120"><i><font color="Green">E77</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E7:120"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> the <a href="abcmiz_0.html#U1" target="_self">adjectives</a> of <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="funct_1.html#T12">FUNCT_1:12</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> as   <a href="abcmiz_0.html#NM2">adjective</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E9:120"/>
( <span class="p1">(<span class="default"><a href="abcmiz_0.html#K7" target="_self">apply</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K7" target="_self">apply</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K7" target="_self">apply</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E6:120"><i><font color="Green">E78</font></i></a>, <a class="ref" href="funct_1.html#T12">FUNCT_1:12</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1">(<span class="default"><a href="abcmiz_0.html#K7" target="_self">apply</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> as   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E11:120"/><i><font color="Green">E79</font></i>: 
( <span class="p1">(<span class="default"><a href="abcmiz_0.html#K7" target="_self">apply</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="abcmiz_0.html#K5" target="_self">ast</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="abcmiz_0.html#R4" target="_self">is_properly_applicable_to</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E2:120"><i><font color="Green">E75</font></i></a>, <a class="txt" href="abcmiz_0.html#E6:120"><i><font color="Green">E78</font></i></a>, <a class="ref" href="abcmiz_0.html#D19" target="_self">Def19</a>, <a class="ref" href="abcmiz_0.html#D28" target="_self">Def28</a></i>;<br/>
<a NAME="E12:120"/>
not <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">c<sub>7</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="120_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:120_1"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:120_1"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 1 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E4:120"><i><font color="Green">E77</font></i></a>, <a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> as    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="abcmiz_0.html#U1" target="_self">adjectives</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="finseq_1.html#T23">FINSEQ_1:23</a></i>;<br/>
<a NAME="E5:120_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="trees_1.html#D1">TREES_1:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E7:120_1"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="trees_1.html#T8">TREES_1:8</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>10</sub></font> as    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="abcmiz_0.html#U1" target="_self">adjectives</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="abcmiz_0.html#E7:120_1"><i><font color="Green">E82</font></i></a>, <a class="ref" href="finseq_1.html#T50">FINSEQ_1:50</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>11</sub></font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> 1</span>)</span> as    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="abcmiz_0.html#U1" target="_self">adjectives</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="finseq_1.html#T23">FINSEQ_1:23</a></i>;<br/>
<a NAME="E10:120_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E4:120"><i><font color="Green">E77</font></i></a>, <a class="txt" href="abcmiz_0.html#E3:120_1"><i><font color="Green">E81</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E11:120_1"/><b>then </b><i><font color="Green">E83</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E7:120_1"><i><font color="Green">E82</font></i></a>, <a class="ref" href="finseq_1.html#T21">FINSEQ_1:21</a>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/>
<a NAME="E12:120_1"/><b>then </b><i><font color="Green">E84</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E4:120"><i><font color="Green">E77</font></i></a>, <a class="txt" href="abcmiz_0.html#E3:120_1"><i><font color="Green">E81</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E13:120_1"/><b>then </b><i><font color="Green">E85</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T21">FINSEQ_1:21</a></i>;<br/>
<a NAME="E14:120_1"/><b>then </b><i><font color="Green">E86</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/>
<a NAME="E15:120_1"/><b>then </b><i><font color="Green">E87</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>;<br/>
<a NAME="E16:120_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> the <a href="abcmiz_0.html#U1" target="_self">adjectives</a> of <font color="Maroon">c<sub>1</sub></font>
 
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>12</sub></font> <a href="funct_1.html#K1">.</a> 1 as   <a href="abcmiz_0.html#NM2">adjective</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E18:120_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="trees_1.html#D1">TREES_1:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>14</sub></font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E20:120_1"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="ref" href="trees_1.html#T8">TREES_1:8</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>14</sub></font> as    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="abcmiz_0.html#U1" target="_self">adjectives</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="abcmiz_0.html#E20:120_1"><i><font color="Green">E88</font></i></a>, <a class="ref" href="finseq_1.html#T50">FINSEQ_1:50</a></i>;<br/>
<a NAME="E22:120_1"/><i><font color="Green">E89</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E12:120_1"><i><font color="Green">E84</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<i><font color="Green">E90</font></i>: <font color="Maroon">c<sub>13</sub></font> = 
<font color="Maroon">c<sub>11</sub></font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="abcmiz_0.html#E14:120_1"><i><font color="Green">E86</font></i></a>, <a class="txt" href="abcmiz_0.html#E20:120_1"><i><font color="Green">E88</font></i></a>, <a class="ref" href="finseq_1.html#T58">FINSEQ_1:58</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="abcmiz_0.html#E3:120_1"><i><font color="Green">E81</font></i></a>, <a class="txt" href="abcmiz_0.html#E7:120_1"><i><font color="Green">E82</font></i></a>, <a class="txt" href="abcmiz_0.html#E11:120_1"><i><font color="Green">E83</font></i></a>, <a class="txt" href="abcmiz_0.html#E22:120_1"><i><font color="Green">E89</font></i></a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
;<br/>
<a NAME="E24:120_1"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="abcmiz_0.html#R5" target="_self">is_properly_applicable_to</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E2:120"><i><font color="Green">E75</font></i></a>, <a class="txt" href="abcmiz_0.html#E7:120_1"><i><font color="Green">E82</font></i></a>, <a class="txt" href="abcmiz_0.html#E11:120_1"><i><font color="Green">E83</font></i></a>, <a class="ref" href="abcmiz_0.html#T61" target="_self">Th61</a></i>;<br/>
<a NAME="E25:120_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="abcmiz_0.html#K8" target="_self">ast</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E3:120_1"><i><font color="Green">E81</font></i></a>, <a class="txt" href="abcmiz_0.html#E7:120_1"><i><font color="Green">E82</font></i></a>, <a class="txt" href="abcmiz_0.html#E11:120_1"><i><font color="Green">E83</font></i></a>, <a class="ref" href="abcmiz_0.html#T37" target="_self">Th37</a></i>;<br/>
<b>then </b><i><font color="Green">E92</font></i>: <font color="Maroon">c<sub>9</sub></font> <a href="abcmiz_0.html#K8" target="_self">ast</a> <font color="Maroon">c<sub>2</sub></font> = 
<font color="Maroon">c<sub>6</sub></font> <a href="abcmiz_0.html#K5" target="_self">ast</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="abcmiz_0.html#K8" target="_self">ast</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="abcmiz_0.html#E1:120_1"><i><font color="Green">E80</font></i></a>, <a class="ref" href="abcmiz_0.html#T25" target="_self">Th25</a></i>
<br/>.= 
<font color="Maroon">c<sub>12</sub></font> <a href="abcmiz_0.html#K8" target="_self">ast</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="abcmiz_0.html#K8" target="_self">ast</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="abcmiz_0.html#E14:120_1"><i><font color="Green">E86</font></i></a>, <a class="txt" href="abcmiz_0.html#E23:120_1"><i><font color="Green">E90</font></i></a>, <a class="ref" href="abcmiz_0.html#T32" target="_self">Th32</a></i>
;<br/>
<a NAME="E27:120_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="abcmiz_0.html#R5" target="_self">is_properly_applicable_to</a> <font color="Maroon">c<sub>9</sub></font> <a href="abcmiz_0.html#K8" target="_self">ast</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E2:120"><i><font color="Green">E75</font></i></a>, <a class="txt" href="abcmiz_0.html#E7:120_1"><i><font color="Green">E82</font></i></a>, <a class="ref" href="abcmiz_0.html#T61" target="_self">Th61</a></i>;<br/>
<a NAME="E28:120_1"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> <a href="abcmiz_0.html#R5" target="_self">is_properly_applicable_to</a> <font color="Maroon">c<sub>9</sub></font> <a href="abcmiz_0.html#K8" target="_self">ast</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E20:120_1"><i><font color="Green">E88</font></i></a>, <a class="txt" href="abcmiz_0.html#E26:120_1"><i><font color="Green">E92</font></i></a>, <a class="ref" href="abcmiz_0.html#T61" target="_self">Th61</a></i>;<br/>
<a NAME="E29:120_1"/><b>then </b><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>15</sub></font> <a href="abcmiz_0.html#R5" target="_self">is_properly_applicable_to</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E24:120_1"><i><font color="Green">E91</font></i></a>, <a class="ref" href="abcmiz_0.html#T62" target="_self">Th62</a></i>;<br/>
<a NAME="E30:120_1"/><b>then </b><i><font color="Green">E94</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>15</sub></font> <a href="abcmiz_0.html#R3" target="_self">is_applicable_to</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="abcmiz_0.html#R3" target="_self">is_applicable_to</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E2:120"><i><font color="Green">E75</font></i></a>, <a class="ref" href="abcmiz_0.html#T58" target="_self">Th58</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>16</sub></font> =  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="abcmiz_0.html#U1" target="_self">adjectives</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<font color="Maroon">c<sub>4</sub></font> <a href="abcmiz_0.html#K8" target="_self">ast</a> <font color="Maroon">c<sub>2</sub></font> = 
<font color="Maroon">c<sub>11</sub></font> <a href="abcmiz_0.html#K8" target="_self">ast</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="abcmiz_0.html#K8" target="_self">ast</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="abcmiz_0.html#E7:120_1"><i><font color="Green">E82</font></i></a>, <a class="ref" href="abcmiz_0.html#T38" target="_self">Th38</a></i>
<br/>.= 
<font color="Maroon">c<sub>15</sub></font> <a href="abcmiz_0.html#K8" target="_self">ast</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="abcmiz_0.html#K8" target="_self">ast</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="abcmiz_0.html#E20:120_1"><i><font color="Green">E88</font></i></a>, <a class="txt" href="abcmiz_0.html#E26:120_1"><i><font color="Green">E92</font></i></a>, <a class="ref" href="abcmiz_0.html#T38" target="_self">Th38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="abcmiz_0.html#K8" target="_self">ast</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="abcmiz_0.html#T38" target="_self">Th38</a></i>
;<br/>
<b>then </b><i><font color="Green">E95</font></i>: <font color="Maroon">c<sub>3</sub></font> <a href="abcmiz_0.html#K6" target="_self">ast</a> <font color="Maroon">c<sub>2</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="abcmiz_0.html#K8" target="_self">ast</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="abcmiz_0.html#E2:120"><i><font color="Green">E75</font></i></a>, <a class="txt" href="abcmiz_0.html#E30:120_1"><i><font color="Green">E94</font></i></a>, <a class="ref" href="abcmiz_0.html#T57" target="_self">Th57</a></i>
<br/>.= 
<font color="Maroon">c<sub>16</sub></font> <a href="abcmiz_0.html#K6" target="_self">ast</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="abcmiz_0.html#E30:120_1"><i><font color="Green">E94</font></i></a>, <a class="ref" href="abcmiz_0.html#T57" target="_self">Th57</a></i>
;<br/>
<a NAME="E34:120_1"/><i><font color="Green">E96</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="abcmiz_0.html#R6" target="_self">is_properly_applicable_to</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E29:120_1"><i><font color="Green">E93</font></i></a>, <a class="ref" href="abcmiz_0.html#D29" target="_self">Def29</a></i>;<br/>
<a NAME="E35:120_1"/><i><font color="Green">E97</font></i>: 
( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="finsub_1.html#K1">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="finsub_1.html#K1">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finsub_1.html#K1">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E2:120"><i><font color="Green">E75</font></i></a>, <a class="txt" href="abcmiz_0.html#E7:120_1"><i><font color="Green">E82</font></i></a>, <a class="txt" href="abcmiz_0.html#E20:120_1"><i><font color="Green">E88</font></i></a>, <a class="ref" href="finseq_1.html#T44">FINSEQ_1:44</a></i>;<br/>
<a NAME="E36:120_1"/><b>then </b>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>15</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E37:120_1"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E35:120_1"><i><font color="Green">E97</font></i></a>, <a class="ref" href="xboole_1.html#T9">XBOOLE_1:9</a></i>;<br/>
<a NAME="E38:120_1"/><b>then </b><i><font color="Green">E98</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E1:120"><i><font color="Green">E74</font></i></a>, <a class="txt" href="abcmiz_0.html#E33:120_1"><i><font color="Green">E95</font></i></a>, <a class="txt" href="abcmiz_0.html#E34:120_1"><i><font color="Green">E96</font></i></a></i>;<br/>
<a NAME="E39:120_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E15:120_1"><i><font color="Green">E87</font></i></a>, <a class="txt" href="abcmiz_0.html#E23:120_1"><i><font color="Green">E90</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E40:120_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E35:120_1"><i><font color="Green">E97</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E41:120_1"/><b>then </b><i><font color="Green">E99</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E35:120_1"><i><font color="Green">E97</font></i></a>, <a class="txt" href="abcmiz_0.html#E38:120_1"><i><font color="Green">E98</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="120_1_5"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:120_1_5"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>9</sub></font> or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>15</sub></font> )
 </span><b>by </b><i><a class="txt" href="abcmiz_0.html#E35:120_1"><i><font color="Green">E97</font></i></a>, <a class="txt" href="abcmiz_0.html#E41:120_1"><i><font color="Green">E99</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="120_1_5_1"><b>suppose </b></a><a NAME="E1:120_1_5_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>17</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:120_1_5_1"/><i><font color="Green">E100</font></i>: 
( <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>17</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="abcmiz_0.html#E3:120_1_5_1"><i><font color="Green">E100</font></i></a></i>;<br/><a NAME="E5:120_1_5_1"/>
(  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>9</sub></font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E7:120_1"><i><font color="Green">E82</font></i></a>, <a class="txt" href="abcmiz_0.html#E3:120_1_5_1"><i><font color="Green">E100</font></i></a>, <a class="ref" href="finseq_1.html#T39">FINSEQ_1:39</a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E6:120_1_5_1"/><b>then </b>
( <font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E3:120_1"><i><font color="Green">E81</font></i></a>, <a class="txt" href="abcmiz_0.html#E7:120_1"><i><font color="Green">E82</font></i></a>, <a class="txt" href="abcmiz_0.html#E11:120_1"><i><font color="Green">E83</font></i></a>, <a class="txt" href="abcmiz_0.html#E3:120_1_5_1"><i><font color="Green">E100</font></i></a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><a NAME="E7:120_1_5_1"/>
contradiction
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E6:120"><i><font color="Green">E78</font></i></a>, <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="120_1_5_2"><b>suppose </b></a><a NAME="E1:120_1_5_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>15</sub></font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>17</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:120_1_5_2"/><i><font color="Green">E100</font></i>: 
( <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>17</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="abcmiz_0.html#E3:120_1_5_2"><i><font color="Green">E100</font></i></a></i>;<br/><a NAME="E5:120_1_5_2"/>
<font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E3:120_1_5_2"><i><font color="Green">E100</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E6:120_1_5_2"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><a NAME="E7:120_1_5_2"/><b>then </b><i><font color="Green">E101</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K2">+</a> 0 )
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E3:120_1"><i><font color="Green">E81</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E8:120_1_5_2"/>
( 1 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E13:120_1"><i><font color="Green">E85</font></i></a>, <a class="txt" href="abcmiz_0.html#E20:120_1"><i><font color="Green">E88</font></i></a>, <a class="txt" href="abcmiz_0.html#E3:120_1_5_2"><i><font color="Green">E100</font></i></a>, <a class="ref" href="finseq_1.html#T41">FINSEQ_1:41</a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/><a NAME="E9:120_1_5_2"/><b>then </b>
( <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E7:120_1"><i><font color="Green">E82</font></i></a>, <a class="txt" href="abcmiz_0.html#E11:120_1"><i><font color="Green">E83</font></i></a>, <a class="ref" href="finseq_1.html#T41">FINSEQ_1:41</a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/><b>hence </b><a NAME="E10:120_1_5_2"/>
contradiction
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E6:120"><i><font color="Green">E78</font></i></a>, <a class="txt" href="abcmiz_0.html#E7:120_1_5_2"><i><font color="Green">E101</font></i></a>, <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>hence </b><a NAME="E13:120"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="abcmiz_0.html#K7" target="_self">apply</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="abcmiz_0.html#K7" target="_self">apply</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="abcmiz_0.html#K11" target="_self">@--&gt;</a> 
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E11:120"><i><font color="Green">E79</font></i></a>, <a class="ref" href="abcmiz_0.html#D31" target="_self">Def31</a></i>;<br/>


</div>
