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

<b>let </b><font color="Maroon" title="c1">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">L</font> being <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a><br/> for <font color="Olive" title="b2">O</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a><br/> for <font color="Olive" title="b3">d</font> being  <a href="lattice5.html#NM3" title="LATTICE5:NM.3">BiFunction</a> of <font color="Maroon" title="c1">A</font>,<font color="Olive" title="b1">L</font>  st <font color="Olive" title="b3">d</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a> holds <br/>for <font color="Olive" title="b4">q</font> being   <a href="lattice5.html#M1" title="LATTICE5:mode.1">QuadrSeq</a> of <font color="Olive" title="b3">d</font> holds   <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Olive" title="b4">q</font>,<font color="Olive" title="b2">O</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a></span><br/><b>let </b><font color="Maroon" title="c2">L</font> be  <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">O</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a><br/> for <font color="Olive" title="b2">d</font> being  <a href="lattice5.html#NM3" title="LATTICE5:NM.3">BiFunction</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">L</font>  st <font color="Olive" title="b2">d</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a> holds <br/>for <font color="Olive" title="b3">q</font> being   <a href="lattice5.html#M1" title="LATTICE5:mode.1">QuadrSeq</a> of <font color="Olive" title="b2">d</font> holds   <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Olive" title="b3">q</font>,<font color="Olive" title="b1">O</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a></span><br/><b>let </b><font color="Maroon" title="c3">O</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">d</font> being  <a href="lattice5.html#NM3" title="LATTICE5:NM.3">BiFunction</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">L</font>  st <font color="Olive" title="b1">d</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a> holds <br/>for <font color="Olive" title="b2">q</font> being   <a href="lattice5.html#M1" title="LATTICE5:mode.1">QuadrSeq</a> of <font color="Olive" title="b1">d</font> holds   <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Olive" title="b2">q</font>,<font color="Maroon" title="c3">O</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a></span><br/><b>let </b><font color="Maroon" title="c4">d</font> be   <a href="lattice5.html#NM3" title="LATTICE5:NM.3">BiFunction</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">d</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a> implies for <font color="Olive" title="b1">q</font> being   <a href="lattice5.html#M1" title="LATTICE5:mode.1">QuadrSeq</a> of <font color="Maroon" title="c4">d</font> holds   <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Olive" title="b1">q</font>,<font color="Maroon" title="c3">O</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a> )</span><br/>







<b>assume </b><a NAME="E1:65"/><i><font color="Green" title="E49">A1</font></i>: 
<font color="Maroon" title="c4">d</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">q</font> being   <a href="lattice5.html#M1" title="LATTICE5:mode.1">QuadrSeq</a> of <font color="Maroon" title="c4">d</font> holds   <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Olive" title="b1">q</font>,<font color="Maroon" title="c3">O</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a></span><br/>

<b>let </b><font color="Maroon" title="c5">q</font> be    <a href="lattice5.html#M1" title="LATTICE5:mode.1">QuadrSeq</a> of <font color="Maroon" title="c4">d</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c3">O</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a></span><br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>] <b>means </b> <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,$1 is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a>;<br/>
<a NAME="E2:65"/><i><font color="Green" title="E50">A2</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c7">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice5.html#D6" target="_self" title="LATTICE5:def.6">LATTICE5:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c6">x</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c8">x'</font> = <font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c9">y'</font> = <font color="Maroon" title="c7">y</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font> <b>by </b><i><a class="ref" href="lattice5.html#T24" target="_self" title="LATTICE5:th.24">Th24</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font> = 
<font color="Maroon" title="c4">d</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c8">x'</font>,<font color="Maroon" title="c9">y'</font>
<b>by </b><i><a class="ref" href="lattice5.html#T29" target="_self" title="LATTICE5:th.29">Th29</a></i>
<br/>.= 
<font color="Maroon" title="c4">d</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c9">y'</font>,<font color="Maroon" title="c8">x'</font>
<b>by </b><i><a class="txt" href="lattice5.html#E1:65"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="lattice5.html#D6" target="_self" title="LATTICE5:def.6">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c6">x</font>
<b>by </b><i><a class="ref" href="lattice5.html#T29" target="_self" title="LATTICE5:th.29">Th29</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:65"/><i><font color="Green" title="E51">A3</font></i>: 
for <font color="Olive" title="b1">O1</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">O1</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[ <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Olive" title="b1">O1</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">O1</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">O1</font>] implies <font color="Maroon">S<sub>1</sub></font>[ <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c6">O1</font>] )</span><br/>

<b>assume </b><a NAME="E1:65_2"/>
 <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">O1</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[ <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c6">O1</font>]</span><br/>

<a NAME="E2:65_2"/><b>then </b><i><font color="Green" title="E52">A4</font></i>: 
 <a href="lattice5.html#K7" title="LATTICE5:func.7">new_bi_fun</a> <span class="p1">(<span class="default"><a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">O1</font></span>)</span>,<span class="p1">(<span class="default"><a href="lattice5.html#K10" title="LATTICE5:func.10">Quadr</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">O1</font></span>)</span> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a>
 
<b>by </b><i><a class="ref" href="lattice5.html#T19" target="_self" title="LATTICE5:th.19">Th19</a></i>;<br/>
<b>let </b><font color="Maroon" title="c7">x</font>, <font color="Maroon" title="c8">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c6">O1</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice5.html#D6" target="_self" title="LATTICE5:def.6">LATTICE5:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c6">O1</font></span>)</span></span>)</span> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c7">x</font>,<font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c6">O1</font></span>)</span></span>)</span> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c8">y</font>,<font color="Maroon" title="c7">x</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c9">x'</font> = <font color="Maroon" title="c7">x</font>, <font color="Maroon" title="c10">y'</font> = <font color="Maroon" title="c8">y</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="lattice5.html#K6" title="LATTICE5:func.6">new_set</a> <span class="p1">(<span class="default"><a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c6">O1</font></span>)</span> <b>by </b><i><a class="ref" href="lattice5.html#T25" target="_self" title="LATTICE5:th.25">Th25</a></i>;<br/>
<i><font color="Green" title="E53">A5</font></i>:  <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c6">O1</font></span>)</span> = 
 <a href="lattice5.html#K7" title="LATTICE5:func.7">new_bi_fun</a> <span class="p1">(<span class="default"><a href="lattice5.html#K11" title="LATTICE5:func.11">BiFun</a> <span class="p2">(<span class="default"><a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">O1</font></span>)</span>,<span class="p2">(<span class="default"><a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c6">O1</font></span>)</span>,<font color="Maroon" title="c2">L</font></span>)</span>,<span class="p1">(<span class="default"><a href="lattice5.html#K10" title="LATTICE5:func.10">Quadr</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">O1</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice5.html#T30" target="_self" title="LATTICE5:th.30">Th30</a></i>
<br/>.= 
 <a href="lattice5.html#K7" title="LATTICE5:func.7">new_bi_fun</a> <span class="p1">(<span class="default"><a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">O1</font></span>)</span>,<span class="p1">(<span class="default"><a href="lattice5.html#K10" title="LATTICE5:func.10">Quadr</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">O1</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice5.html#D16" target="_self" title="LATTICE5:def.16">Def16</a></i>
;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c6">O1</font></span>)</span></span>)</span> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c7">x</font>,<font color="Maroon" title="c8">y</font> = 
<span class="p1">(<span class="default"><a href="lattice5.html#K7" title="LATTICE5:func.7">new_bi_fun</a> <span class="p2">(<span class="default"><a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">O1</font></span>)</span>,<span class="p2">(<span class="default"><a href="lattice5.html#K10" title="LATTICE5:func.10">Quadr</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">O1</font></span>)</span></span>)</span> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c10">y'</font>,<font color="Maroon" title="c9">x'</font>
<b>by </b><i><a class="txt" href="lattice5.html#E2:65_2"><i><font color="Green" title="E52">A4</font></i></a>, <a class="ref" href="lattice5.html#D6" target="_self" title="LATTICE5:def.6">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c6">O1</font></span>)</span></span>)</span> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c8">y</font>,<font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="lattice5.html#E4:65_2"><i><font color="Green" title="E53">A5</font></i></a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E4:65"/><i><font color="Green" title="E52">A6</font></i>: 
for <font color="Olive" title="b1">O2</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>  st <font color="Olive" title="b1">O2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b1">O2</font> <a href="ordinal1.html#NR2" title="ORDINAL1:NR.2">is_limit_ordinal</a>  &amp; ( for <font color="Olive" title="b2">O1</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>  st <font color="Olive" title="b2">O1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">O2</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b2">O1</font>] ) holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">O2</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">O2</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">O2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c6">O2</font> <a href="ordinal1.html#NR2" title="ORDINAL1:NR.2">is_limit_ordinal</a>  &amp; ( for <font color="Olive" title="b1">O1</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>  st <font color="Olive" title="b1">O1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">O2</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">O1</font>] ) implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">O2</font>] )</span><br/>

<b>assume </b><a NAME="E1:65_3"/><i><font color="Green" title="E53">A7</font></i>: 
( <font color="Maroon" title="c6">O2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c6">O2</font> <a href="ordinal1.html#NR2" title="ORDINAL1:NR.2">is_limit_ordinal</a>  &amp; ( for <font color="Olive" title="b1">O1</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>  st <font color="Olive" title="b1">O1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">O2</font> holds <br/> <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Olive" title="b1">O1</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">O2</font>]</span><br/>

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>) <b>-&gt; </b>  <a href="lattice5.html#NM3" title="LATTICE5:NM.3">BiFunction</a> of <span class="p1">(<span class="default"><a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,$1</span>)</span>,<font color="Maroon" title="c2">L</font> =  <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,$1;<br/>
<b>consider </b><font color="Maroon" title="c7">Ls</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">T-Sequence</a><b> such that </b><br/><a NAME="E3:65_3"/><i><font color="Green" title="E54">A8</font></i>: 
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c7">Ls</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">O2</font> &amp; ( for <font color="Olive" title="b1">O1</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>  st <font color="Olive" title="b1">O1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">O2</font> holds <br/><font color="Maroon" title="c7">Ls</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">O1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">O1</font>) ) )
 <b>from </b><i><a class="ref" href="ordinal2.html#S2" title="ORDINAL2:sch.2">ORDINAL2:sch 2</a>();<br/></i>
<a NAME="E4:65_3"/><i><font color="Green" title="E55">A9</font></i>: 
 <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">O2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c7">Ls</font></span>)</span>
 
<b>by </b><i><a class="txt" href="lattice5.html#E1:65_3"><i><font color="Green" title="E53">A7</font></i></a>, <a class="txt" href="lattice5.html#E3:65_3"><i><font color="Green" title="E54">A8</font></i></a>, <a class="ref" href="lattice5.html#T31" target="_self" title="LATTICE5:th.31">Th31</a></i>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>) <b>-&gt; </b>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  =  <a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,$1;<br/>
<b>consider </b><font color="Maroon" title="c8">Ts</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">T-Sequence</a><b> such that </b><br/><a NAME="E6:65_3"/><i><font color="Green" title="E56">A10</font></i>: 
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">Ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">O2</font> &amp; ( for <font color="Olive" title="b1">O1</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>  st <font color="Olive" title="b1">O1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">O2</font> holds <br/><font color="Maroon" title="c8">Ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">O1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive" title="b1">O1</font>) ) )
 <b>from </b><i><a class="ref" href="ordinal2.html#S2" title="ORDINAL2:sch.2">ORDINAL2:sch 2</a>();<br/></i>
<a NAME="E7:65_3"/><i><font color="Green" title="E57">A11</font></i>: 
 <a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c6">O2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c8">Ts</font></span>)</span>
 
<b>by </b><i><a class="txt" href="lattice5.html#E1:65_3"><i><font color="Green" title="E53">A7</font></i></a>, <a class="txt" href="lattice5.html#E6:65_3"><i><font color="Green" title="E56">A10</font></i></a>, <a class="ref" href="lattice5.html#T26" target="_self" title="LATTICE5:th.26">Th26</a></i>;<br/>
<b>set </b><font color="Maroon" title="c9">CS</font> =  <a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c6">O2</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">f</font> =  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c7">Ls</font></span>)</span> as   <a href="lattice5.html#NM3" title="LATTICE5:NM.3">BiFunction</a> of <span class="p1">(<span class="default"><a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c6">O2</font></span>)</span>,<font color="Maroon" title="c2">L</font> <b>by </b><i><a class="txt" href="lattice5.html#E4:65_3"><i><font color="Green" title="E55">A9</font></i></a></i>;<br/>
<a NAME="E9:65_3"/>
<font color="Maroon" title="c10">f</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c11">x</font>, <font color="Maroon" title="c12">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c6">O2</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice5.html#D6" target="_self" title="LATTICE5:def.6">LATTICE5:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c10">f</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c11">x</font></span><br/>

<b>consider </b><font color="Maroon" title="c13">x1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E2:65_3_1"/><i><font color="Green" title="E58">A12</font></i>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">x1</font> &amp; <font color="Maroon" title="c13">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c8">Ts</font> )
 <b>by </b><i><a class="txt" href="lattice5.html#E7:65_3"><i><font color="Green" title="E57">A11</font></i></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c14">o1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:65_3_1"/><i><font color="Green" title="E59">A13</font></i>: 
( <font color="Maroon" title="c14">o1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">Ts</font> &amp; <font color="Maroon" title="c13">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">Ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">o1</font> )
 <b>by </b><i><a class="txt" href="lattice5.html#E2:65_3_1"><i><font color="Green" title="E58">A12</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c15">y1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:65_3_1"/><i><font color="Green" title="E60">A14</font></i>: 
( <font color="Maroon" title="c12">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c15">y1</font> &amp; <font color="Maroon" title="c15">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c8">Ts</font> )
 <b>by </b><i><a class="txt" href="lattice5.html#E7:65_3"><i><font color="Green" title="E57">A11</font></i></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c16">o2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E8:65_3_1"/><i><font color="Green" title="E61">A15</font></i>: 
( <font color="Maroon" title="c16">o2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">Ts</font> &amp; <font color="Maroon" title="c15">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">Ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">o2</font> )
 <b>by </b><i><a class="txt" href="lattice5.html#E6:65_3_1"><i><font color="Green" title="E60">A14</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c17">o1</font> = <font color="Maroon" title="c14">o1</font>, <font color="Maroon" title="c18">o2</font> = <font color="Maroon" title="c16">o2</font> as   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> <b>by </b><i><a class="txt" href="lattice5.html#E4:65_3_1"><i><font color="Green" title="E59">A13</font></i></a>, <a class="txt" href="lattice5.html#E8:65_3_1"><i><font color="Green" title="E61">A15</font></i></a>, <a class="ref" href="ordinal1.html#T23" title="ORDINAL1:th.23">ORDINAL1:23</a></i>;<br/>
<a NAME="E10:65_3_1"/><i><font color="Green" title="E62">A16</font></i>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c17">o1</font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E6:65_3"><i><font color="Green" title="E56">A10</font></i></a>, <a class="txt" href="lattice5.html#E2:65_3_1"><i><font color="Green" title="E58">A12</font></i></a>, <a class="txt" href="lattice5.html#E4:65_3_1"><i><font color="Green" title="E59">A13</font></i></a></i>;<br/>
<a NAME="E11:65_3_1"/><i><font color="Green" title="E63">A17</font></i>: 
<font color="Maroon" title="c12">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c18">o2</font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E6:65_3"><i><font color="Green" title="E56">A10</font></i></a>, <a class="txt" href="lattice5.html#E6:65_3_1"><i><font color="Green" title="E60">A14</font></i></a>, <a class="txt" href="lattice5.html#E8:65_3_1"><i><font color="Green" title="E61">A15</font></i></a></i>;<br/>
<a NAME="E12:65_3_1"/><i><font color="Green" title="E64">A18</font></i>: 
<font color="Maroon" title="c7">Ls</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c17">o1</font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E3:65_3"><i><font color="Green" title="E54">A8</font></i></a>, <a class="txt" href="lattice5.html#E6:65_3"><i><font color="Green" title="E56">A10</font></i></a>, <a class="txt" href="lattice5.html#E4:65_3_1"><i><font color="Green" title="E59">A13</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c19">h1</font> = <font color="Maroon" title="c7">Ls</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">o1</font> as   <a href="lattice5.html#NM3" title="LATTICE5:NM.3">BiFunction</a> of <span class="p1">(<span class="default"><a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c17">o1</font></span>)</span>,<font color="Maroon" title="c2">L</font> ;<br/>
<a NAME="E14:65_3_1"/><i><font color="Green" title="E65">A19</font></i>: 
<font color="Maroon" title="c19">h1</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_3_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c20">x</font>, <font color="Maroon" title="c21">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c17">o1</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice5.html#D6" target="_self" title="LATTICE5:def.6">LATTICE5:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c19">h1</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c20">x</font>,<font color="Maroon" title="c21">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">h1</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c21">y</font>,<font color="Maroon" title="c20">x</font></span><br/>

<a NAME="E1:65_3_1_1"/><i><font color="Green" title="E66">A20</font></i>: 
 <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c17">o1</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a>
 
<b>by </b><i><a class="txt" href="lattice5.html#E1:65_3"><i><font color="Green" title="E53">A7</font></i></a>, <a class="txt" href="lattice5.html#E6:65_3"><i><font color="Green" title="E56">A10</font></i></a>, <a class="txt" href="lattice5.html#E4:65_3_1"><i><font color="Green" title="E59">A13</font></i></a></i>;<br/>
<b>thus </b><font color="Maroon" title="c19">h1</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c20">x</font>,<font color="Maroon" title="c21">y</font> = 
<span class="p1">(<span class="default"><a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c17">o1</font></span>)</span> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c20">x</font>,<font color="Maroon" title="c21">y</font>
<b>by </b><i><a class="txt" href="lattice5.html#E3:65_3"><i><font color="Green" title="E54">A8</font></i></a>, <a class="txt" href="lattice5.html#E6:65_3"><i><font color="Green" title="E56">A10</font></i></a>, <a class="txt" href="lattice5.html#E4:65_3_1"><i><font color="Green" title="E59">A13</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c17">o1</font></span>)</span> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c21">y</font>,<font color="Maroon" title="c20">x</font>
<b>by </b><i><a class="txt" href="lattice5.html#E1:65_3_1_1"><i><font color="Green" title="E66">A20</font></i></a>, <a class="ref" href="lattice5.html#D6" target="_self" title="LATTICE5:def.6">Def6</a></i>
<br/>.= 
<font color="Maroon" title="c19">h1</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c21">y</font>,<font color="Maroon" title="c20">x</font>
<b>by </b><i><a class="txt" href="lattice5.html#E3:65_3"><i><font color="Green" title="E54">A8</font></i></a>, <a class="txt" href="lattice5.html#E6:65_3"><i><font color="Green" title="E56">A10</font></i></a>, <a class="txt" href="lattice5.html#E4:65_3_1"><i><font color="Green" title="E59">A13</font></i></a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E15:65_3_1"/><i><font color="Green" title="E66">A21</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c19">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c17">o1</font></span>)</span>,<span class="p2">(<span class="default"><a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c17">o1</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E16:65_3_1"/><i><font color="Green" title="E67">A22</font></i>: 
<font color="Maroon" title="c7">Ls</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c18">o2</font>
 
<b>by </b><i><a class="txt" href="lattice5.html#E3:65_3"><i><font color="Green" title="E54">A8</font></i></a>, <a class="txt" href="lattice5.html#E6:65_3"><i><font color="Green" title="E56">A10</font></i></a>, <a class="txt" href="lattice5.html#E8:65_3_1"><i><font color="Green" title="E61">A15</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c20">h2</font> = <font color="Maroon" title="c7">Ls</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">o2</font> as   <a href="lattice5.html#NM3" title="LATTICE5:NM.3">BiFunction</a> of <span class="p1">(<span class="default"><a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c18">o2</font></span>)</span>,<font color="Maroon" title="c2">L</font> ;<br/>
<a NAME="E18:65_3_1"/><i><font color="Green" title="E68">A23</font></i>: 
<font color="Maroon" title="c20">h2</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_3_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c21">x</font>, <font color="Maroon" title="c22">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c18">o2</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice5.html#D6" target="_self" title="LATTICE5:def.6">LATTICE5:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c20">h2</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c21">x</font>,<font color="Maroon" title="c22">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">h2</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c22">y</font>,<font color="Maroon" title="c21">x</font></span><br/>

<a NAME="E1:65_3_1_2"/><i><font color="Green" title="E69">A24</font></i>: 
 <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c18">o2</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a>
 
<b>by </b><i><a class="txt" href="lattice5.html#E1:65_3"><i><font color="Green" title="E53">A7</font></i></a>, <a class="txt" href="lattice5.html#E6:65_3"><i><font color="Green" title="E56">A10</font></i></a>, <a class="txt" href="lattice5.html#E8:65_3_1"><i><font color="Green" title="E61">A15</font></i></a></i>;<br/>
<b>thus </b><font color="Maroon" title="c20">h2</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c21">x</font>,<font color="Maroon" title="c22">y</font> = 
<span class="p1">(<span class="default"><a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c18">o2</font></span>)</span> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c21">x</font>,<font color="Maroon" title="c22">y</font>
<b>by </b><i><a class="txt" href="lattice5.html#E3:65_3"><i><font color="Green" title="E54">A8</font></i></a>, <a class="txt" href="lattice5.html#E6:65_3"><i><font color="Green" title="E56">A10</font></i></a>, <a class="txt" href="lattice5.html#E8:65_3_1"><i><font color="Green" title="E61">A15</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c18">o2</font></span>)</span> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c22">y</font>,<font color="Maroon" title="c21">x</font>
<b>by </b><i><a class="txt" href="lattice5.html#E1:65_3_1_2"><i><font color="Green" title="E69">A24</font></i></a>, <a class="ref" href="lattice5.html#D6" target="_self" title="LATTICE5:def.6">Def6</a></i>
<br/>.= 
<font color="Maroon" title="c20">h2</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c22">y</font>,<font color="Maroon" title="c21">x</font>
<b>by </b><i><a class="txt" href="lattice5.html#E3:65_3"><i><font color="Green" title="E54">A8</font></i></a>, <a class="txt" href="lattice5.html#E6:65_3"><i><font color="Green" title="E56">A10</font></i></a>, <a class="txt" href="lattice5.html#E8:65_3_1"><i><font color="Green" title="E61">A15</font></i></a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E19:65_3_1"/><i><font color="Green" title="E69">A25</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c20">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c18">o2</font></span>)</span>,<span class="p2">(<span class="default"><a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c18">o2</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_3_1_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:65_3_1_3"/>
( <font color="Maroon" title="c17">o1</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c18">o2</font> or <font color="Maroon" title="c18">o2</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c17">o1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_3_1_3_1"><b>suppose </b></a><a NAME="E1:65_3_1_3_1"/>
<font color="Maroon" title="c17">o1</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c18">o2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c10">f</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c11">x</font></span><br/><div class="add"><a NAME="E2:65_3_1_3_1"/><b>then </b><i><font color="Green" title="E70">A26</font></i>: 
 <a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c17">o1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c18">o2</font>
 <b>by </b><i><a class="ref" href="lattice5.html#T32" target="_self" title="LATTICE5:th.32">Th32</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c21">x'</font> = <font color="Maroon" title="c11">x</font>, <font color="Maroon" title="c22">y'</font> = <font color="Maroon" title="c12">y</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c18">o2</font> <b>by </b><i><a class="txt" href="lattice5.html#E6:65_3"><i><font color="Green" title="E56">A10</font></i></a>, <a class="txt" href="lattice5.html#E6:65_3_1"><i><font color="Green" title="E60">A14</font></i></a>, <a class="txt" href="lattice5.html#E8:65_3_1"><i><font color="Green" title="E61">A15</font></i></a>, <a class="txt" href="lattice5.html#E10:65_3_1"><i><font color="Green" title="E62">A16</font></i></a></i>;<br/><a NAME="E4:65_3_1_3_1"/>
 <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c18">o2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c7">Ls</font>
 <b>by </b><i><a class="txt" href="lattice5.html#E3:65_3"><i><font color="Green" title="E54">A8</font></i></a>, <a class="txt" href="lattice5.html#E6:65_3"><i><font color="Green" title="E56">A10</font></i></a>, <a class="txt" href="lattice5.html#E8:65_3_1"><i><font color="Green" title="E61">A15</font></i></a>, <a class="txt" href="lattice5.html#E16:65_3_1"><i><font color="Green" title="E67">A22</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><a NAME="E5:65_3_1_3_1"/><b>then </b><i><font color="Green" title="E71">A27</font></i>: 
<font color="Maroon" title="c20">h2</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c10">f</font>
 <b>by </b><i><a class="txt" href="lattice5.html#E16:65_3_1"><i><font color="Green" title="E67">A22</font></i></a>, <a class="ref" href="zfmisc_1.html#T92" title="ZFMISC_1:th.92">ZFMISC_1:92</a></i>;<br/><a NAME="E6:65_3_1_3_1"/><i><font color="Green" title="E72">A28</font></i>: 
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c20">h2</font> &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c11">x</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c20">h2</font> )
 <b>by </b><i><a class="txt" href="lattice5.html#E10:65_3_1"><i><font color="Green" title="E62">A16</font></i></a>, <a class="txt" href="lattice5.html#E11:65_3_1"><i><font color="Green" title="E63">A17</font></i></a>, <a class="txt" href="lattice5.html#E19:65_3_1"><i><font color="Green" title="E69">A25</font></i></a>, <a class="txt" href="lattice5.html#E2:65_3_1_3_1"><i><font color="Green" title="E70">A26</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><b>hence </b><font color="Maroon" title="c10">f</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> = 
<font color="Maroon" title="c20">h2</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c21">x'</font>,<font color="Maroon" title="c22">y'</font>
<b>by </b><i><a class="txt" href="lattice5.html#E5:65_3_1_3_1"><i><font color="Green" title="E71">A27</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon" title="c20">h2</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c22">y'</font>,<font color="Maroon" title="c21">x'</font>
<b>by </b><i><a class="txt" href="lattice5.html#E18:65_3_1"><i><font color="Green" title="E68">A23</font></i></a>, <a class="ref" href="lattice5.html#D6" target="_self" title="LATTICE5:def.6">Def6</a></i>
<br/>.= 
<font color="Maroon" title="c10">f</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c11">x</font>
<b>by </b><i><a class="txt" href="lattice5.html#E5:65_3_1_3_1"><i><font color="Green" title="E71">A27</font></i></a>, <a class="txt" href="lattice5.html#E6:65_3_1_3_1"><i><font color="Green" title="E72">A28</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_3_1_3_2"><b>suppose </b></a><a NAME="E1:65_3_1_3_2"/>
<font color="Maroon" title="c18">o2</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c17">o1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c10">f</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c11">x</font></span><br/><div class="add"><a NAME="E2:65_3_1_3_2"/><b>then </b><i><font color="Green" title="E70">A29</font></i>: 
 <a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c18">o2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c17">o1</font>
 <b>by </b><i><a class="ref" href="lattice5.html#T32" target="_self" title="LATTICE5:th.32">Th32</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c21">x'</font> = <font color="Maroon" title="c11">x</font>, <font color="Maroon" title="c22">y'</font> = <font color="Maroon" title="c12">y</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="lattice5.html#K9" title="LATTICE5:func.9">ConsecutiveSet</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c17">o1</font> <b>by </b><i><a class="txt" href="lattice5.html#E6:65_3"><i><font color="Green" title="E56">A10</font></i></a>, <a class="txt" href="lattice5.html#E2:65_3_1"><i><font color="Green" title="E58">A12</font></i></a>, <a class="txt" href="lattice5.html#E4:65_3_1"><i><font color="Green" title="E59">A13</font></i></a>, <a class="txt" href="lattice5.html#E11:65_3_1"><i><font color="Green" title="E63">A17</font></i></a></i>;<br/><a NAME="E4:65_3_1_3_2"/>
 <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c17">o1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c7">Ls</font>
 <b>by </b><i><a class="txt" href="lattice5.html#E3:65_3"><i><font color="Green" title="E54">A8</font></i></a>, <a class="txt" href="lattice5.html#E6:65_3"><i><font color="Green" title="E56">A10</font></i></a>, <a class="txt" href="lattice5.html#E4:65_3_1"><i><font color="Green" title="E59">A13</font></i></a>, <a class="txt" href="lattice5.html#E12:65_3_1"><i><font color="Green" title="E64">A18</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><a NAME="E5:65_3_1_3_2"/><b>then </b><i><font color="Green" title="E71">A30</font></i>: 
<font color="Maroon" title="c19">h1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c10">f</font>
 <b>by </b><i><a class="txt" href="lattice5.html#E12:65_3_1"><i><font color="Green" title="E64">A18</font></i></a>, <a class="ref" href="zfmisc_1.html#T92" title="ZFMISC_1:th.92">ZFMISC_1:92</a></i>;<br/><a NAME="E6:65_3_1_3_2"/><i><font color="Green" title="E72">A31</font></i>: 
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c19">h1</font> &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c11">x</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c19">h1</font> )
 <b>by </b><i><a class="txt" href="lattice5.html#E10:65_3_1"><i><font color="Green" title="E62">A16</font></i></a>, <a class="txt" href="lattice5.html#E11:65_3_1"><i><font color="Green" title="E63">A17</font></i></a>, <a class="txt" href="lattice5.html#E15:65_3_1"><i><font color="Green" title="E66">A21</font></i></a>, <a class="txt" href="lattice5.html#E2:65_3_1_3_2"><i><font color="Green" title="E70">A29</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><b>hence </b><font color="Maroon" title="c10">f</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font> = 
<font color="Maroon" title="c19">h1</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c21">x'</font>,<font color="Maroon" title="c22">y'</font>
<b>by </b><i><a class="txt" href="lattice5.html#E5:65_3_1_3_2"><i><font color="Green" title="E71">A30</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon" title="c19">h1</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c22">y'</font>,<font color="Maroon" title="c21">x'</font>
<b>by </b><i><a class="txt" href="lattice5.html#E14:65_3_1"><i><font color="Green" title="E65">A19</font></i></a>, <a class="ref" href="lattice5.html#D6" target="_self" title="LATTICE5:def.6">Def6</a></i>
<br/>.= 
<font color="Maroon" title="c10">f</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c11">x</font>
<b>by </b><i><a class="txt" href="lattice5.html#E5:65_3_1_3_2"><i><font color="Green" title="E71">A30</font></i></a>, <a class="txt" href="lattice5.html#E6:65_3_1_3_2"><i><font color="Green" title="E72">A31</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>hence </b><a NAME="E10:65_3"/>
 <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">O2</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a>
 <b>by </b><i><a class="txt" href="lattice5.html#E1:65_3"><i><font color="Green" title="E53">A7</font></i></a>, <a class="txt" href="lattice5.html#E3:65_3"><i><font color="Green" title="E54">A8</font></i></a>, <a class="ref" href="lattice5.html#T31" target="_self" title="LATTICE5:th.31">Th31</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E5:65"/>
for <font color="Olive" title="b1">O</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">O</font>]
 
<b>from </b><i><a class="ref" href="ordinal2.html#S1" title="ORDINAL2:sch.1">ORDINAL2:sch 1</a>(<a class="txt" href="lattice5.html#E2:65"><i><font color="Green" title="E50">A2</font></i></a>, <a class="txt" href="lattice5.html#E3:65"><i><font color="Green" title="E51">A3</font></i></a>, <a class="txt" href="lattice5.html#E4:65"><i><font color="Green" title="E52">A6</font></i></a>);<br/></i>
<b>hence </b><a NAME="E6:65"/>
 <a href="lattice5.html#K13" title="LATTICE5:func.13">ConsecutiveDelta</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c3">O</font> is <a href="lattice5.html#V1" title="LATTICE5:attr.1">symmetric</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
