<?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> 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">a</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> holds <br/><font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font></span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</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">a</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> )</span><br/>





<b>assume </b><a NAME="E1:13"/><i><font color="Green" title="E6">A1</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</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">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font></span><br/>

<b>consider </b><font color="Maroon" title="c4">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font><b> such that </b><br/><a NAME="E3:13"/><i><font color="Green" title="E7">A2</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="ref" href="midsp_1.html#D4" target="_self" title="MIDSP_1:def.4">Def4</a></i>;<br/>
<font color="Maroon" title="c3">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c3">b</font>
<b>by </b><i><a class="txt" href="#E3:13"><i><font color="Green" title="E7">A2</font></i></a>, <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="c4">x</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c2">a</font>
<b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="midsp_1.html#T15" target="_self" title="MIDSP_1:th.15">Th15</a></i>
<br/>.= 
<font color="Maroon" title="c2">a</font>
<b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="#E3:13"><i><font color="Green" title="E7">A2</font></i></a>, <a class="ref" href="midsp_1.html#T15" target="_self" title="MIDSP_1:th.15">Th15</a></i>
;<br/>
<b>hence </b><a NAME="E5:13"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
