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

<b>let </b><font color="Maroon" title="c1">M</font> be   <a href="midsp_1.html#NM1" title="MIDSP_1:NM.1">MidSp</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">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font>  st <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K6" title="MIDSP_1:func.6">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K6" title="MIDSP_1:func.6">~</a>  holds <br/><font color="Olive" title="b1">a</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Olive" title="b3">c</font></span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">d</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K6" title="MIDSP_1:func.6">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K6" title="MIDSP_1:func.6">~</a>  implies <font color="Maroon" title="c2">a</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c4">c</font> )</span><br/>









<b>assume </b><a NAME="E1:36"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K6" title="MIDSP_1:func.6">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K6" title="MIDSP_1:func.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="c2">a</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c4">c</font></span><br/>

<a NAME="E2:36"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="midsp_1.html#R1" title="MIDSP_1:pred.1">@@</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>
 
<b>by </b><i><a class="ref" href="midsp_1.html#T32" target="_self" title="MIDSP_1:th.32">Th32</a>, <a class="ref" href="midsp_1.html#T43" target="_self" title="MIDSP_1:th.43">Th43</a></i>;<br/>
<b>hence </b><a NAME="E3:36"/>
<font color="Maroon" title="c2">a</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c4">c</font>
 <b>by </b><i><a class="ref" href="midsp_1.html#D5" target="_self" title="MIDSP_1:def.5">Def5</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>
