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

<b>reconsider </b><font color="Maroon">DER</font> = <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> <a href="finseq_2.html#K3">*</a> </span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> as  non <a href="xboole_0.html#V1">empty</a>  <a href="relset_1.html#M2">Relation</a> of <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> <a href="finseq_2.html#K3">*</a> ,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> <b>by </b><i><a class="ref" href="relset_1.html#D1">RELSET_1:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">EM</font> =  <a href="prelamb.html#G2" target="_self">typestr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>,<a href="midsp_1.html#K2">op2</a> ,<a href="midsp_1.html#K2">op2</a> ,<a href="midsp_1.html#K2">op2</a> ,<font color="Maroon">DER</font> #) as  non <a href="struct_0.html#V3">empty</a>  <a href="prelamb.html#L2" target="_self">typestr</a>  <b>by </b><i><a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/>
<b>take </b>
<font color="Maroon">EM</font>
;<br/>

<a NAME="E3:41_1_1"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">x</font> being  <a href="prelamb.html#NM1">type</a> of <font color="Maroon">EM</font><br/> for <font color="Olive">X</font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">EM</font> holds  <font color="Olive">X</font> <a href="prelamb.html#R2" target="_self">==&gt;.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be   <a href="prelamb.html#NM1">type</a> of <font color="Maroon">EM</font>;<br/><b>let </b><font color="Maroon">X</font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">EM</font>;<br/>



<a NAME="E1:41_1_1_1"/>
<span class="p1"><a href="prelamb.html#K6" target="_self">[</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">x</font></span><a href="prelamb.html#K6" target="_self">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> <a href="finseq_2.html#K3">*</a> </span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
;<br/>
<b>hence </b><a NAME="E2:41_1_1_1"/>
<font color="Maroon">X</font> <a href="prelamb.html#R2" target="_self">==&gt;.</a> <font color="Maroon">x</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:41_1_1"/>
for <font color="Olive">x</font> being  <a href="prelamb.html#NM1">type</a> of <font color="Maroon">EM</font> holds  <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">x</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="prelamb.html#R2" target="_self">==&gt;.</a> <font color="Olive">x</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="prelamb.html#D19" target="_self">PRELAMB:def 19</a><br/>

<b>thus </b><a NAME="E5:41_1_1"/>
( ( for <font color="Olive">T</font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">EM</font><br/> for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="prelamb.html#NM1">type</a> of <font color="Maroon">EM</font>  st <font color="Olive">T</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">y</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="prelamb.html#R2" target="_self">==&gt;.</a> <font color="Olive">x</font> holds <br/><font color="Olive">T</font> <a href="prelamb.html#R2" target="_self">==&gt;.</a> <font color="Olive">x</font> <a href="prelamb.html#K2" target="_self">/"</a> <font color="Olive">y</font> ) &amp; ( for <font color="Olive">T</font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">EM</font><br/> for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="prelamb.html#NM1">type</a> of <font color="Maroon">EM</font>  st <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">y</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Olive">T</font> <a href="prelamb.html#R2" target="_self">==&gt;.</a> <font color="Olive">x</font> holds <br/><font color="Olive">T</font> <a href="prelamb.html#R2" target="_self">==&gt;.</a> <font color="Olive">y</font> <a href="prelamb.html#K1" target="_self">\</a> <font color="Olive">x</font> ) &amp; ( for <font color="Olive">T</font>, <font color="Olive">X</font>, <font color="Olive">Y</font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">EM</font><br/> for <font color="Olive">x</font>, <font color="Olive">y</font>, <font color="Olive">z</font> being  <a href="prelamb.html#NM1">type</a> of <font color="Maroon">EM</font>  st <font color="Olive">T</font> <a href="prelamb.html#R2" target="_self">==&gt;.</a> <font color="Olive">y</font> &amp; <span class="p1">(<span class="default"><font color="Olive">X</font> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">x</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Olive">Y</font> <a href="prelamb.html#R2" target="_self">==&gt;.</a> <font color="Olive">z</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">X</font> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Olive">x</font> <a href="prelamb.html#K2" target="_self">/"</a> <font color="Olive">y</font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Olive">T</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Olive">Y</font> <a href="prelamb.html#R2" target="_self">==&gt;.</a> <font color="Olive">z</font> ) &amp; ( for <font color="Olive">T</font>, <font color="Olive">X</font>, <font color="Olive">Y</font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">EM</font><br/> for <font color="Olive">x</font>, <font color="Olive">y</font>, <font color="Olive">z</font> being  <a href="prelamb.html#NM1">type</a> of <font color="Maroon">EM</font>  st <font color="Olive">T</font> <a href="prelamb.html#R2" target="_self">==&gt;.</a> <font color="Olive">y</font> &amp; <span class="p1">(<span class="default"><font color="Olive">X</font> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">x</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Olive">Y</font> <a href="prelamb.html#R2" target="_self">==&gt;.</a> <font color="Olive">z</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">X</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">T</font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Olive">y</font> <a href="prelamb.html#K1" target="_self">\</a> <font color="Olive">x</font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Olive">Y</font> <a href="prelamb.html#R2" target="_self">==&gt;.</a> <font color="Olive">z</font> ) &amp; ( for <font color="Olive">X</font>, <font color="Olive">Y</font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">EM</font><br/> for <font color="Olive">x</font>, <font color="Olive">y</font>, <font color="Olive">z</font> being  <a href="prelamb.html#NM1">type</a> of <font color="Maroon">EM</font>  st <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">X</font> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">x</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">y</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Olive">Y</font> <a href="prelamb.html#R2" target="_self">==&gt;.</a> <font color="Olive">z</font> holds <br/><span class="p1">(<span class="default"><font color="Olive">X</font> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Olive">x</font> <a href="prelamb.html#K3" target="_self">*</a> <font color="Olive">y</font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Olive">Y</font> <a href="prelamb.html#R2" target="_self">==&gt;.</a> <font color="Olive">z</font> ) &amp; ( for <font color="Olive">X</font>, <font color="Olive">Y</font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">EM</font><br/> for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="prelamb.html#NM1">type</a> of <font color="Maroon">EM</font>  st <font color="Olive">X</font> <a href="prelamb.html#R2" target="_self">==&gt;.</a> <font color="Olive">x</font> &amp; <font color="Olive">Y</font> <a href="prelamb.html#R2" target="_self">==&gt;.</a> <font color="Olive">y</font> holds <br/><font color="Olive">X</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">Y</font> <a href="prelamb.html#R2" target="_self">==&gt;.</a> <font color="Olive">x</font> <a href="prelamb.html#K3" target="_self">*</a> <font color="Olive">y</font> ) )
 <b>by </b><i/>;<br/>


</div>
