<?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">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">c</font>, <font color="Olive" title="b6">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 <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="midsp_1.html#R1" title="MIDSP_1:pred.1">@@</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font> &amp; <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="midsp_1.html#R1" title="MIDSP_1:pred.1">@@</a> <font color="Olive" title="b5">c</font>,<font color="Olive" title="b6">d</font> holds <br/><font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font> <a href="midsp_1.html#R1" title="MIDSP_1:pred.1">@@</a> <font color="Olive" title="b5">c</font>,<font color="Olive" title="b6">d</font></span><br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c6">c</font>, <font color="Maroon" title="c7">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"> ( <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="midsp_1.html#R1" title="MIDSP_1:pred.1">@@</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font> &amp; <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="midsp_1.html#R1" title="MIDSP_1:pred.1">@@</a> <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c7">d</font> implies <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font> <a href="midsp_1.html#R1" title="MIDSP_1:pred.1">@@</a> <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c7">d</font> )</span><br/>













<b>assume </b><a NAME="E1:22"/><i><font color="Green" title="E16">A1</font></i>: 
<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="midsp_1.html#R1" title="MIDSP_1:pred.1">@@</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="midsp_1.html#R1" title="MIDSP_1:pred.1">@@</a> <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c7">d</font> or <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font> <a href="midsp_1.html#R1" title="MIDSP_1:pred.1">@@</a> <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c7">d</font> )</span><br/>

<b>assume </b><a NAME="E2:22"/><i><font color="Green" title="E17">A2</font></i>: 
<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="midsp_1.html#R1" title="MIDSP_1:pred.1">@@</a> <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c7">d</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">a</font>,<font color="Maroon" title="c5">b</font> <a href="midsp_1.html#R1" title="MIDSP_1:pred.1">@@</a> <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c7">d</font></span><br/>

<span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c7">d</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c7">d</font></span>)</span>
<b>by </b><i><a class="ref" href="midsp_1.html#D4" target="_self" title="MIDSP_1:def.4">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c7">d</font></span>)</span>
<b>by </b><i><a class="txt" href="midsp_1.html#E1:22"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="midsp_1.html#D5" target="_self" title="MIDSP_1:def.5">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c6">c</font></span>)</span>
<b>by </b><i><a class="txt" href="midsp_1.html#E2:22"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="midsp_1.html#D5" target="_self" title="MIDSP_1:def.5">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c6">c</font></span>)</span>
<b>by </b><i><a class="ref" href="midsp_1.html#D4" target="_self" title="MIDSP_1:def.4">Def4</a></i>
;<br/>
<b>hence </b><a NAME="E4:22"/>
<font color="Maroon" title="c4">a</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c6">c</font>
 <b>by </b><i><a class="ref" href="midsp_1.html#T18" target="_self" title="MIDSP_1:th.18">Th18</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="midsp_1.html#D5" target="_self" title="MIDSP_1:def.5">MIDSP_1:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
