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<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>, <font color="Olive" title="b5">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">a</font>,<font color="Olive" title="b2">b</font> <a href="midsp_1.html#R1" title="MIDSP_1:pred.1">@@</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="midsp_1.html#R1" title="MIDSP_1:pred.1">@@</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b5">d'</font> holds <br/><font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">d'</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>, <font color="Maroon" title="c6">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">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> &amp; <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="c6">d'</font> implies <font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d'</font> )</span><br/>











<b>assume </b><a NAME="E1:21"/><i><font color="Green" title="E15">A1</font></i>: 
<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>
 ; <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">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="c6">d'</font> or <font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d'</font> )</span><br/>

<b>assume </b><a NAME="E2:21"/><i><font color="Green" title="E16">A2</font></i>: 
<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="c6">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="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d'</font></span><br/>

<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> = 
<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="txt" href="#E1:21"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="midsp_1.html#D5" target="_self" title="MIDSP_1:def.5">Def5</a></i>
<br/>.= 
<font color="Maroon" title="c2">a</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c6">d'</font>
<b>by </b><i><a class="txt" href="#E2:21"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="midsp_1.html#D5" target="_self" title="MIDSP_1:def.5">Def5</a></i>
;<br/>
<b>hence </b><a NAME="E4:21"/>
<font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d'</font>
 <b>by </b><i><a class="ref" href="midsp_1.html#T18" target="_self" title="MIDSP_1:th.18">Th18</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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