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<span class="kw">let </span><font color="Maroon" title="c1">OAS</font> be   <a href="analoaf.html#NM1" title="ANALOAF:NM.1">OAffinSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">OAS</font> is  <a href="pasch.html#V3" title="PASCH:attr.3">satisfying_Gen_Par_Pasch</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="pasch.html#D3" target="_self" title="PASCH:def.3">PASCH:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">c</font>, <font color="Olive" title="b3">a9</font>, <font color="Olive" title="b4">b9</font>, <font color="Olive" title="b5">c9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font>  st not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">b</font>,<font color="Olive" title="b3">a9</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Olive" title="b3">a9</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b1">b</font>,<font color="Olive" title="b4">b9</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Olive" title="b3">a9</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b2">c</font>,<font color="Olive" title="b5">c9</font> &amp;  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">c</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Olive" title="b3">a9</font>,<font color="Olive" title="b4">b9</font>,<font color="Olive" title="b5">c9</font> holds <br/> <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Olive" title="b3">a9</font>,<font color="Olive" title="b4">b9</font>,<font color="Olive" title="b5">c9</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">a9</font>, <font color="Maroon" title="c6">b9</font>, <font color="Maroon" title="c7">c9</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a9</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">a9</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">b9</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">a9</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">c9</font> &amp;  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font>,<font color="Maroon" title="c7">c9</font> implies  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font>,<font color="Maroon" title="c7">c9</font> )</span><br/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:24"/><span class="lab"><font color="Green" title="E8">A1</font></span>: 
not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a9</font>
 <span class="kw">and </span><br/><a NAME="E2:24"/><span class="lab"><font color="Green" title="E9">A2</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">a9</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">b9</font>
 <span class="kw">and </span><br/><a NAME="E3:24"/><span class="lab"><font color="Green" title="E10">A3</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">a9</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">c9</font>
 <span class="kw">and </span><br/><a NAME="E4:24"/><span class="lab"><font color="Green" title="E11">A4</font></span>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">and </span><br/><a NAME="E5:24"/><span class="lab"><font color="Green" title="E12">A5</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font>,<font color="Maroon" title="c7">c9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font>,<font color="Maroon" title="c7">c9</font></span><br/>

<span class="kw">thus </span><a NAME="E6:24"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font>,<font color="Maroon" title="c7">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E2:24"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="txt" href="#E3:24"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="txt" href="#E4:24"><span class="lab"><font color="Green" title="E11">A4</font></span></a>, <a class="txt" href="#E5:24"><span class="lab"><font color="Green" title="E12">A5</font></span></a>, <a class="ref" href="pasch.html#T17" target="_self" title="PASCH:th.17">Th17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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