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<div><span class="kw">theorem </span><a NAME="T9"><span class="comment"><font color="firebrick">:: SEMI_AF1:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">SAS</font> being   <a href="semi_af1.html#NM1" title="SEMI_AF1:NM.1">Semi_Affine_Space</a><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">SAS</font>  st  not <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">d</font> holds <br/>( <font color="Olive" title="b2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b4">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">a</font> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="semi_af1.html#D1" target="_self" onmouseover="rs('semi_af1/D1')" onmouseout="rh()">Def1</a>, <a class="ref" href="semi_af1.html#T1" target="_self" onmouseover="rs('semi_af1/T1')" onmouseout="rh()">Th1</a>, <a class="ref" href="semi_af1.html#T3" target="_self" onmouseover="rs('semi_af1/T3')" onmouseout="rh()">Th3</a></span>;<br/></div></div>
