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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="yellow_0.html#V1">lower-bounded</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="lattice5.html#NM3">BiFunction</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>





<b>assume </b><a NAME="E1:40"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="lattice5.html#V2">zeroed</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="lattice5.html#M1">QuadrSeq</a> of <font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>



<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="ordinal1.html#NM2">Ordinal</a>] means  <a href="lattice8.html#K6" target="_self">ConsecutiveDelta2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">a<sub>1</sub></font> is <a href="lattice5.html#V2">zeroed</a>;<br/>
<a NAME="E2:40"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="xboole_0.html#K1">{}</a> ]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="40_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">c<sub>1</sub></font>,<a href="xboole_0.html#K1">{}</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice5.html#D7">LATTICE5:def 7</a><br/>

<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="lattice8.html#T15" target="_self">Th15</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="lattice8.html#K6" target="_self">ConsecutiveDelta2</a> <font color="Maroon">c<sub>4</sub></font>,<a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="lattice5.html#K4">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>6</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="lattice5.html#K4">.</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="lattice8.html#T19" target="_self">Th19</a></i>
<br/>.= 
 <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="lattice8.html#E1:40"><i><font color="Green">E33</font></i></a>, <a class="ref" href="lattice5.html#D7">LATTICE5:def 7</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E3:40"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[ <a href="ordinal1.html#K1">succ</a> <font color="Olive">b<sub>1</sub></font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="40_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>

<b>assume </b><a NAME="E1:40_2"/>
 <a href="lattice8.html#K6" target="_self">ConsecutiveDelta2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> is <a href="lattice5.html#V2">zeroed</a>
 ;<br/>

<a NAME="E2:40_2"/><b>then </b><i><font color="Green">E36</font></i>: 
 <a href="lattice8.html#K2" target="_self">new_bi_fun2</a> <span class="p1">(<span class="default"><a href="lattice8.html#K6" target="_self">ConsecutiveDelta2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="lattice8.html#K4" target="_self">Quadr2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> is <a href="lattice5.html#V2">zeroed</a>
 
<b>by </b><i><a class="ref" href="lattice8.html#T10" target="_self">Th10</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1">succ</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice5.html#D7">LATTICE5:def 7</a><br/>

<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>7</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="lattice8.html#K1" target="_self">new_set2</a> <span class="p1">(<span class="default"><a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <b>by </b><i><a class="ref" href="lattice8.html#T16" target="_self">Th16</a></i>;<br/>
 <a href="lattice8.html#K6" target="_self">ConsecutiveDelta2</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1">succ</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> = 
 <a href="lattice8.html#K2" target="_self">new_bi_fun2</a> <span class="p1">(<span class="default"><a href="lattice5.html#K11">BiFun</a> <span class="p2">(<span class="default"><a href="lattice8.html#K6" target="_self">ConsecutiveDelta2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="lattice8.html#K4" target="_self">Quadr2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="lattice8.html#T20" target="_self">Th20</a></i>
<br/>.= 
 <a href="lattice8.html#K2" target="_self">new_bi_fun2</a> <span class="p1">(<span class="default"><a href="lattice8.html#K6" target="_self">ConsecutiveDelta2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="lattice8.html#K4" target="_self">Quadr2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="lattice5.html#D16">LATTICE5:def 16</a></i>
;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="lattice8.html#K6" target="_self">ConsecutiveDelta2</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><a href="ordinal1.html#K1">succ</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="lattice5.html#K4">.</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><a href="lattice8.html#K2" target="_self">new_bi_fun2</a> <span class="p2">(<span class="default"><a href="lattice8.html#K6" target="_self">ConsecutiveDelta2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="lattice8.html#K4" target="_self">Quadr2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="lattice5.html#K4">.</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>8</sub></font>

<br/>.= 
 <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="lattice8.html#E2:40_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="lattice5.html#D7">LATTICE5:def 7</a></i>
;<br/><br/>


</div><b>end;</b></div>
<a NAME="E4:40"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Olive">b<sub>1</sub></font> <a href="ordinal1.html#NR2" target="_self">is_limit_ordinal</a>  &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>2</sub></font>] ) holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="40_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>

<b>assume </b><a NAME="E1:40_3"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>6</sub></font> <a href="ordinal1.html#NR2" target="_self">is_limit_ordinal</a>  &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> holds <br/> <a href="lattice8.html#K6" target="_self">ConsecutiveDelta2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font> is <a href="lattice5.html#V2">zeroed</a> ) )
 ;<br/>

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="ordinal1.html#NM2">Ordinal</a>) <b>-&gt; </b>  <a href="lattice5.html#NM3">BiFunction</a> of <span class="p1">(<span class="default"><a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">a<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> =  <a href="lattice8.html#K6" target="_self">ConsecutiveDelta2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">a<sub>1</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="ordinal1.html#NM3">T-Sequence</a><b> such that </b><br/><a NAME="E3:40_3"/><i><font color="Green">E38</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> holds <br/><font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>) ) )
 <b>from </b><i><a class="ref" href="ordinal2.html#S2">ORDINAL2:sch 2</a>();<br/></i>
<a NAME="E4:40_3"/><i><font color="Green">E39</font></i>: 
 <a href="lattice8.html#K6" target="_self">ConsecutiveDelta2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="lattice8.html#E1:40_3"><i><font color="Green">E37</font></i></a>, <a class="txt" href="lattice8.html#E3:40_3"><i><font color="Green">E38</font></i></a>, <a class="ref" href="lattice8.html#T21" target="_self">Th21</a></i>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(  <a href="ordinal1.html#NM2">Ordinal</a>) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  =  <a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">a<sub>1</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="ordinal1.html#NM3">T-Sequence</a><b> such that </b><br/><a NAME="E6:40_3"/><i><font color="Green">E40</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> holds <br/><font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>1</sub></font>) ) )
 <b>from </b><i><a class="ref" href="ordinal2.html#S2">ORDINAL2:sch 2</a>();<br/></i>
<a NAME="E7:40_3"/><i><font color="Green">E41</font></i>: 
 <a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="lattice8.html#E1:40_3"><i><font color="Green">E37</font></i></a>, <a class="txt" href="lattice8.html#E6:40_3"><i><font color="Green">E40</font></i></a>, <a class="ref" href="lattice8.html#T17" target="_self">Th17</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> =  <a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> =  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> as   <a href="lattice5.html#NM3">BiFunction</a> of <span class="p1">(<span class="default"><a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="lattice8.html#E4:40_3"><i><font color="Green">E39</font></i></a></i>;<br/>
<a NAME="E9:40_3"/>
<font color="Maroon">c<sub>10</sub></font> is <a href="lattice5.html#V2">zeroed</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="40_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>11</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice5.html#D7">LATTICE5:def 7</a><br/>

<b>consider </b><font color="Maroon">c<sub>12</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:40_3_1"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="txt" href="lattice8.html#E7:40_3"><i><font color="Green">E41</font></i></a>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>13</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:40_3_1"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font> )
 <b>by </b><i><a class="txt" href="lattice8.html#E2:40_3_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>13</sub></font> as   <a href="ordinal1.html#NM2">Ordinal</a> <b>by </b><i><a class="txt" href="lattice8.html#E4:40_3_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="ordinal1.html#T23">ORDINAL1:23</a></i>;<br/>
<a NAME="E6:40_3_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="lattice8.html#E6:40_3"><i><font color="Green">E40</font></i></a>, <a class="txt" href="lattice8.html#E2:40_3_1"><i><font color="Green">E42</font></i></a>, <a class="txt" href="lattice8.html#E4:40_3_1"><i><font color="Green">E43</font></i></a></i>;<br/>
<a NAME="E7:40_3_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a>  <a href="lattice8.html#K6" target="_self">ConsecutiveDelta2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="lattice8.html#E3:40_3"><i><font color="Green">E38</font></i></a>, <a class="txt" href="lattice8.html#E6:40_3"><i><font color="Green">E40</font></i></a>, <a class="txt" href="lattice8.html#E4:40_3_1"><i><font color="Green">E43</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> as   <a href="lattice5.html#NM3">BiFunction</a> of <span class="p1">(<span class="default"><a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> ;<br/>
<a NAME="E9:40_3_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>15</sub></font> is <a href="lattice5.html#V2">zeroed</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="40_3_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>16</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>14</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice5.html#D7">LATTICE5:def 7</a><br/>

<a NAME="E1:40_3_1_1"/><i><font color="Green">E47</font></i>: 
 <a href="lattice8.html#K6" target="_self">ConsecutiveDelta2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>14</sub></font> is <a href="lattice5.html#V2">zeroed</a>
 
<b>by </b><i><a class="txt" href="lattice8.html#E1:40_3"><i><font color="Green">E37</font></i></a>, <a class="txt" href="lattice8.html#E6:40_3"><i><font color="Green">E40</font></i></a>, <a class="txt" href="lattice8.html#E4:40_3_1"><i><font color="Green">E43</font></i></a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>15</sub></font> <a href="lattice5.html#K4">.</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>16</sub></font> = 
<span class="p1">(<span class="default"><a href="lattice8.html#K6" target="_self">ConsecutiveDelta2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="lattice5.html#K4">.</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>16</sub></font>
<b>by </b><i><a class="txt" href="lattice8.html#E3:40_3"><i><font color="Green">E38</font></i></a>, <a class="txt" href="lattice8.html#E6:40_3"><i><font color="Green">E40</font></i></a>, <a class="txt" href="lattice8.html#E4:40_3_1"><i><font color="Green">E43</font></i></a></i>
<br/>.= 
 <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="lattice8.html#E1:40_3_1_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="lattice5.html#D7">LATTICE5:def 7</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E10:40_3_1"/>
 <a href="lattice8.html#K6" target="_self">ConsecutiveDelta2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="lattice8.html#E3:40_3"><i><font color="Green">E38</font></i></a>, <a class="txt" href="lattice8.html#E6:40_3"><i><font color="Green">E40</font></i></a>, <a class="txt" href="lattice8.html#E4:40_3_1"><i><font color="Green">E43</font></i></a>, <a class="txt" href="lattice8.html#E7:40_3_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E11:40_3_1"/><b>then </b><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="lattice8.html#E7:40_3_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="zfmisc_1.html#T92">ZFMISC_1:92</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>11</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>14</sub></font> <b>by </b><i><a class="txt" href="lattice8.html#E6:40_3"><i><font color="Green">E40</font></i></a>, <a class="txt" href="lattice8.html#E2:40_3_1"><i><font color="Green">E42</font></i></a>, <a class="txt" href="lattice8.html#E4:40_3_1"><i><font color="Green">E43</font></i></a></i>;<br/>
<a NAME="E13:40_3_1"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>14</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="lattice8.html#K3" target="_self">ConsecutiveSet2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>14</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E14:40_3_1"/><b>then </b><i><font color="Green">E48</font></i>: 
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="txt" href="lattice8.html#E6:40_3_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>10</sub></font> <a href="lattice5.html#K4">.</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>11</sub></font> = 
<font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="domain_1.html#K1">]</a></span>

<br/>.= 
<font color="Maroon">c<sub>15</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="txt" href="lattice8.html#E11:40_3_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="lattice8.html#E14:40_3_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon">c<sub>15</sub></font> <a href="lattice5.html#K4">.</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>16</sub></font>

<br/>.= 
 <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="lattice8.html#E9:40_3_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="lattice5.html#D7">LATTICE5:def 7</a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E10:40_3"/>
 <a href="lattice8.html#K6" target="_self">ConsecutiveDelta2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> is <a href="lattice5.html#V2">zeroed</a>
 <b>by </b><i><a class="txt" href="lattice8.html#E1:40_3"><i><font color="Green">E37</font></i></a>, <a class="txt" href="lattice8.html#E3:40_3"><i><font color="Green">E38</font></i></a>, <a class="ref" href="lattice8.html#T21" target="_self">Th21</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:40"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="ordinal1.html#NM2">Ordinal</a> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="ordinal2.html#S1">ORDINAL2:sch 1</a>(<a class="txt" href="lattice8.html#E2:40"><i><font color="Green">E34</font></i></a>, <a class="txt" href="lattice8.html#E3:40"><i><font color="Green">E35</font></i></a>, <a class="txt" href="lattice8.html#E4:40"><i><font color="Green">E36</font></i></a>);<br/></i>
<b>hence </b><a NAME="E6:40"/>
 <a href="lattice8.html#K6" target="_self">ConsecutiveDelta2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> is <a href="lattice5.html#V2">zeroed</a>
 ;<br/>


</div>
