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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E30">Th38</font></span>: <a NAME="T38"><span class="comment"><font color="firebrick">:: SEMI_AF1:38</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">a1</font>, <font color="Olive" title="b3">a2</font>, <font color="Olive" title="b4">a3</font>, <font color="Olive" title="b5">a4</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">SAS</font>  st  <a href="semi_af1.html#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Olive" title="b2">a1</font>,<font color="Olive" title="b3">a2</font>,<font color="Olive" title="b4">a3</font>,<font color="Olive" title="b5">a4</font> holds <br/>(  not <font color="Olive" title="b2">a1</font>,<font color="Olive" title="b3">a2</font>,<font color="Olive" title="b4">a3</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b2">a1</font>,<font color="Olive" title="b4">a3</font>,<font color="Olive" title="b3">a2</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b2">a1</font>,<font color="Olive" title="b3">a2</font>,<font color="Olive" title="b5">a4</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b2">a1</font>,<font color="Olive" title="b5">a4</font>,<font color="Olive" title="b3">a2</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b2">a1</font>,<font color="Olive" title="b4">a3</font>,<font color="Olive" title="b5">a4</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b2">a1</font>,<font color="Olive" title="b5">a4</font>,<font color="Olive" title="b4">a3</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b3">a2</font>,<font color="Olive" title="b2">a1</font>,<font color="Olive" title="b4">a3</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b3">a2</font>,<font color="Olive" title="b4">a3</font>,<font color="Olive" title="b2">a1</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b3">a2</font>,<font color="Olive" title="b2">a1</font>,<font color="Olive" title="b5">a4</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b3">a2</font>,<font color="Olive" title="b5">a4</font>,<font color="Olive" title="b2">a1</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b3">a2</font>,<font color="Olive" title="b4">a3</font>,<font color="Olive" title="b5">a4</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b3">a2</font>,<font color="Olive" title="b5">a4</font>,<font color="Olive" title="b4">a3</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b4">a3</font>,<font color="Olive" title="b2">a1</font>,<font color="Olive" title="b3">a2</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b4">a3</font>,<font color="Olive" title="b3">a2</font>,<font color="Olive" title="b2">a1</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b4">a3</font>,<font color="Olive" title="b2">a1</font>,<font color="Olive" title="b5">a4</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b4">a3</font>,<font color="Olive" title="b5">a4</font>,<font color="Olive" title="b2">a1</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b4">a3</font>,<font color="Olive" title="b3">a2</font>,<font color="Olive" title="b5">a4</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b4">a3</font>,<font color="Olive" title="b5">a4</font>,<font color="Olive" title="b3">a2</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b5">a4</font>,<font color="Olive" title="b2">a1</font>,<font color="Olive" title="b3">a2</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b5">a4</font>,<font color="Olive" title="b3">a2</font>,<font color="Olive" title="b2">a1</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b5">a4</font>,<font color="Olive" title="b2">a1</font>,<font color="Olive" title="b4">a3</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b5">a4</font>,<font color="Olive" title="b4">a3</font>,<font color="Olive" title="b2">a1</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b5">a4</font>,<font color="Olive" title="b3">a2</font>,<font color="Olive" title="b4">a3</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  &amp;  not <font color="Olive" title="b5">a4</font>,<font color="Olive" title="b4">a3</font>,<font color="Olive" title="b3">a2</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">are_collinear</a>  )</div></div>
