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

<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="membered.html#V6" title="MEMBERED:attr.6">natural-membered</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">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon" title="c1">X</font> <a href="afinsq_2.html#R1" title="AFINSQ_2:pred.1">&lt;N&lt;</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <font color="Maroon" title="c1">X</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">i</font></span><br/><b>let </b><font color="Maroon" title="c3">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> <a href="afinsq_2.html#R1" title="AFINSQ_2:pred.1">&lt;N&lt;</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <font color="Maroon" title="c1">X</font></span>)</span> implies <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">i</font> )</span><br/>



<b>assume </b><a NAME="E1:55"/><i><font color="Green" title="E37">A1</font></i>: 
( <font color="Maroon" title="c1">X</font> <a href="afinsq_2.html#R1" title="AFINSQ_2:pred.1">&lt;N&lt;</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <font color="Maroon" title="c1">X</font></span>)</span> )
 ; <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="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">i</font></span><br/>

<a NAME="E2:55"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="card_1.html#T27" title="CARD_1:th.27">CARD_1:27</a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E3:55"/><b>then </b><i><font color="Green" title="E38">A102</font></i>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">X</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T40" title="NAT_1:th.40">NAT_1:40</a></i>;<br/>
<a NAME="E4:55"/><i><font color="Green" title="E39">A56</font></i>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="afinsq_2.html#T31" target="_self" title="AFINSQ_2:th.31">Th44</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">h</font> = <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span> <a href="card_fin.html#K4" title="CARD_FIN:func.4">|</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> as   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/>
<a NAME="E6:55"/><i><font color="Green" title="E40">A230bn</font></i>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="afinsq_2.html#T31" target="_self" title="AFINSQ_2:th.31">Th44</a></i>;<br/>
<a NAME="E7:55"/><b>then </b><i><font color="Green" title="E41">A230b</font></i>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <font color="Maroon" title="c1">X</font></span>)</span>
 
<b>by </b><i><a class="ref" href="afinsq_2.html#T12" target="_self" title="AFINSQ_2:th.12">TH80</a>, <a class="txt" href="#E3:55"><i><font color="Green" title="E38">A102</font></i></a>, <a class="txt" href="#E4:55"><i><font color="Green" title="E39">A56</font></i></a></i>;<br/>
<a NAME="E8:55"/><i><font color="Green" title="E42">A230</font></i>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="afinsq_2.html#T12" target="_self" title="AFINSQ_2:th.12">TH80</a>, <a class="txt" href="#E3:55"><i><font color="Green" title="E38">A102</font></i></a>, <a class="txt" href="#E4:55"><i><font color="Green" title="E39">A56</font></i></a>, <a class="txt" href="#E6:55"><i><font color="Green" title="E40">A230bn</font></i></a></i>;<br/>
<a NAME="E9:55"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">X</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E3:55"><i><font color="Green" title="E38">A102</font></i></a>, <a class="ref" href="afinsq_2.html#T31" target="_self" title="AFINSQ_2:th.31">Th44</a></i>;<br/>
<a NAME="E10:55"/><b>then </b><i><font color="Green" title="E43">A101</font></i>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="afinsq_2.html#T31" target="_self" title="AFINSQ_2:th.31">Th44</a></i>;<br/>
<a NAME="E11:55"/><i><font color="Green" title="E44">A100</font></i>: 
for <font color="Olive" title="b1">l</font>, <font color="Olive" title="b2">m</font>, <font color="Olive" title="b3">k1</font>, <font color="Olive" title="b4">k2</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">l</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">m</font> &amp; <font color="Olive" title="b2">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c4">h</font> &amp; <font color="Olive" title="b3">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">l</font> &amp; <font color="Olive" title="b4">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b2">m</font> holds <br/><font color="Olive" title="b3">k1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b4">k2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">l</font>, <font color="Maroon" title="c6">m</font>, <font color="Maroon" title="c7">k1</font>, <font color="Maroon" title="c8">k2</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">l</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">m</font> &amp; <font color="Maroon" title="c6">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c4">h</font> &amp; <font color="Maroon" title="c7">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">l</font> &amp; <font color="Maroon" title="c8">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font> implies <font color="Maroon" title="c7">k1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">k2</font> )</span><br/>

<b>assume </b><a NAME="E1:55_1"/><i><font color="Green" title="E45">B1</font></i>: 
( <font color="Maroon" title="c5">l</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">m</font> &amp; <font color="Maroon" title="c6">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c4">h</font> &amp; <font color="Maroon" title="c7">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">l</font> &amp; <font color="Maroon" title="c8">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">k1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">k2</font></span><br/>

<a NAME="E2:55_1"/>
<font color="Maroon" title="c5">l</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="txt" href="#E1:55_1"><i><font color="Green" title="E45">B1</font></i></a>, <a class="txt" href="#E8:55"><i><font color="Green" title="E42">A230</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E3:55_1"/><b>then </b><i><font color="Green" title="E46">B3</font></i>: 
<font color="Maroon" title="c4">h</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">l</font>
 
<b>by </b><i><a class="txt" href="#E1:55"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="afinsq_2.html#T38" target="_self" title="AFINSQ_2:th.38">AE221e</a>, <a class="txt" href="#E4:55"><i><font color="Green" title="E39">A56</font></i></a></i>;<br/>
<a NAME="E4:55_1"/><i><font color="Green" title="E47">B4</font></i>: 
<font color="Maroon" title="c4">h</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">m</font>
 
<b>by </b><i><a class="txt" href="#E1:55"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="afinsq_2.html#T38" target="_self" title="AFINSQ_2:th.38">AE221e</a>, <a class="txt" href="#E1:55_1"><i><font color="Green" title="E45">B1</font></i></a>, <a class="txt" href="#E4:55"><i><font color="Green" title="E39">A56</font></i></a>, <a class="txt" href="#E7:55"><i><font color="Green" title="E41">A230b</font></i></a></i>;<br/>
<a NAME="E5:55_1"/>
<font color="Maroon" title="c6">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:55_1"><i><font color="Green" title="E45">B1</font></i></a>, <a class="txt" href="#E7:55"><i><font color="Green" title="E41">A230b</font></i></a>, <a class="txt" href="#E10:55"><i><font color="Green" title="E43">A101</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<b>hence </b><a NAME="E6:55_1"/>
<font color="Maroon" title="c7">k1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">k2</font>
 <b>by </b><i><a class="txt" href="#E3:55_1"><i><font color="Green" title="E46">B3</font></i></a>, <a class="txt" href="#E4:55_1"><i><font color="Green" title="E47">B4</font></i></a>, <a class="ref" href="afinsq_2.html#D5" target="_self" title="AFINSQ_2:def.5">AC113</a>, <a class="txt" href="#E1:55_1"><i><font color="Green" title="E45">B1</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="E12:55"/><i><font color="Green" title="E45">A103</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="txt" href="#E1:55"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="afinsq_2.html#T38" target="_self" title="AFINSQ_2:th.38">AE221e</a>, <a class="txt" href="#E4:55"><i><font color="Green" title="E39">A56</font></i></a></i>;<br/>
<a NAME="E13:55"/>
<font color="Maroon" title="c4">h</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">i</font>
 
<b>by </b><i><a class="txt" href="#E1:55"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="afinsq_2.html#T38" target="_self" title="AFINSQ_2:th.38">AE221e</a>, <a class="txt" href="#E4:55"><i><font color="Green" title="E39">A56</font></i></a></i>;<br/>
<b>hence </b><a NAME="E14:55"/>
<span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K9" title="AFINSQ_2:func.9">Sgm0</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">i</font>
 <b>by </b><i><a class="ref" href="afinsq_2.html#D5" target="_self" title="AFINSQ_2:def.5">AC113</a>, <a class="txt" href="#E11:55"><i><font color="Green" title="E44">A100</font></i></a>, <a class="txt" href="#E12:55"><i><font color="Green" title="E45">A103</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>
