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

<span class="kw">let </span><font color="Maroon" title="c2">S1</font>, <font color="Maroon" title="c3">S2</font> be   <a href="stacks_1.html#NM2" title="STACKS_1:NM.2">stack</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="stacks_1.html#K14" title="STACKS_1:func.14">/==</a></span>)</span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="stacks_1.html#D15" target="_self" title="STACKS_1:def.15">STACKS_1:def 15</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">S1</font> <a href="stacks_1.html#R2" title="STACKS_1:pred.2">==</a> <font color="Maroon" title="c3">S2</font> implies <font color="Maroon" title="c2">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">S2</font> )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c4">s1</font> being   <a href="stacks_1.html#NM2" title="STACKS_1:NM.2">stack</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:82_1_1"/><span class="lab"><font color="Green" title="E56">A1</font></span>: 
<font color="Maroon" title="c2">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span>,<font color="Maroon" title="c4">s1</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="stacks_1.html#T34" target="_self" title="STACKS_1:th.34">Th70</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">s2</font> being   <a href="stacks_1.html#NM2" title="STACKS_1:NM.2">stack</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E4:82_1_1"/><span class="lab"><font color="Green" title="E57">A2</font></span>: 
<font color="Maroon" title="c3">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font></span>)</span>,<font color="Maroon" title="c5">s2</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="stacks_1.html#T34" target="_self" title="STACKS_1:th.34">Th70</a></span>;<br/>
<span class="kw">assume </span><a NAME="E5:82_1_1"/>
<span class="p1"><a href="stacks_1.html#K9" title="STACKS_1:func.9">|.</a><span class="default"><font color="Maroon" title="c2">S1</font></span><a href="stacks_1.html#K9" title="STACKS_1:func.9">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="stacks_1.html#K9" title="STACKS_1:func.9">|.</a><span class="default"><font color="Maroon" title="c3">S2</font></span><a href="stacks_1.html#K9" title="STACKS_1:func.9">.|</a></span>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="stacks_1.html#D14" target="_self" title="STACKS_1:def.14">STACKS_1:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">S2</font></span><br/>

<span class="kw">then </span><span class="p1"><a href="stacks_1.html#K9" title="STACKS_1:func.9">|.</a><span class="default"><font color="Maroon" title="c4">s1</font></span><a href="stacks_1.html#K9" title="STACKS_1:func.9">.|</a></span> = 
<span class="p1"><a href="stacks_1.html#K9" title="STACKS_1:func.9">|.</a><span class="default"><font color="Maroon" title="c3">S2</font></span><a href="stacks_1.html#K9" title="STACKS_1:func.9">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:82_1_1"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="ref" href="stacks_1.html#T41" target="_self" title="STACKS_1:th.41">Th80</a></span>
<br/>.= 
<span class="p1"><a href="stacks_1.html#K9" title="STACKS_1:func.9">|.</a><span class="default"><font color="Maroon" title="c5">s2</font></span><a href="stacks_1.html#K9" title="STACKS_1:func.9">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:82_1_1"><span class="lab"><font color="Green" title="E57">A2</font></span></a>, <a class="ref" href="stacks_1.html#T41" target="_self" title="STACKS_1:th.41">Th80</a></span>
;<br/>
<a NAME="E7:82_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">s1</font> <a href="stacks_1.html#R2" title="STACKS_1:pred.2">==</a> <font color="Maroon" title="c5">s2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="stacks_1.html#D14" target="_self" title="STACKS_1:def.14">CONG</a></span>;<br/>
<a NAME="E8:82_1_1"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">s1</font>,<font color="Maroon" title="c5">s2</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="stacks_1.html#K10" title="STACKS_1:func.10">==_</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="stacks_1.html#D16" target="_self" title="STACKS_1:def.16">REL</a></span>;<br/>
<a NAME="E9:82_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">s2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:82_1_1"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="ref" href="eqrel_1.html#T18" title="EQREL_1:th.18">EQREL_1:18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:82_1_1"/>
<font color="Maroon" title="c2">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">S2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:82_1_1"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="txt" href="#E4:82_1_1"><span class="lab"><font color="Green" title="E57">A2</font></span></a>, <a class="ref" href="eqrel_1.html#T23" title="EQREL_1:th.23">EQREL_1:23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
