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<b>let </b><font color="Maroon" title="c1">SAS</font> be   <a href="semi_af1.html#NM1" title="SEMI_AF1:NM.1">Semi_Affine_Space</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">p</font>, <font color="Olive" title="b4">q</font>, <font color="Olive" title="b5">c</font>, <font color="Olive" title="b6">s</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font>  st  <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font> &amp;  <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b5">c</font>,<font color="Olive" title="b4">q</font>,<font color="Olive" title="b6">s</font> holds <br/> <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b5">c</font>,<font color="Olive" title="b3">p</font>,<font color="Olive" title="b6">s</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">p</font>, <font color="Maroon" title="c5">q</font>, <font color="Maroon" title="c6">c</font>, <font color="Maroon" title="c7">s</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font> &amp;  <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">s</font> implies  <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c7">s</font> )</span><br/>













<b>assume </b><a NAME="E1:73"/>
(  <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font> &amp;  <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">s</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c7">s</font></span><br/>

<a NAME="E2:73"/><b>then </b>
(  <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">p</font> &amp;  <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c7">s</font> )
 
<b>by </b><i><a class="ref" href="semi_af1.html#T89" target="_self" title="SEMI_AF1:th.89">Th89</a></i>;<br/>
<a NAME="E3:73"/><b>then </b>
 <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c7">s</font>
 
<b>by </b><i><a class="ref" href="semi_af1.html#T85" target="_self" title="SEMI_AF1:th.85">Th85</a></i>;<br/>
<b>hence </b><a NAME="E4:73"/>
 <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c7">s</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T88" target="_self" title="SEMI_AF1:th.88">Th88</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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