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<div>:: <span class="kw">deftheorem </span>   defines <a href="geomtrap.html#V4" title="GEOMTRAP:attr.4">TrapSpace-like</a> <a onclick="hs(this)" href="javascript:()">GEOMTRAP:def 14 : <br/></a><span> for <font color="Olive" title="b1">IT</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="analoaf.html#L1" title="ANALOAF:struct.1">AffinStruct</a>  holds <br/> ( <font color="Olive" title="b1">IT</font> is  <a href="geomtrap.html#V4" title="GEOMTRAP:attr.4">TrapSpace-like</a>  iff  for <font color="Olive" title="b2">a9</font>, <font color="Olive" title="b3">b9</font>, <font color="Olive" title="b4">c9</font>, <font color="Olive" title="b5">d9</font>, <font color="Olive" title="b6">p9</font>, <font color="Olive" title="b7">q9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">IT</font> holds <br/> ( <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b3">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">b9</font>,<font color="Olive" title="b2">a9</font> &amp; ( <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b3">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">c9</font>,<font color="Olive" title="b5">d9</font> &amp; <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b3">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">c9</font>,<font color="Olive" title="b7">q9</font> &amp;  not <font color="Olive" title="b2">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">b9</font> implies <font color="Olive" title="b5">d9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">q9</font> ) &amp; ( <font color="Olive" title="b6">p9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b7">q9</font> &amp; <font color="Olive" title="b6">p9</font>,<font color="Olive" title="b7">q9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b3">b9</font> &amp; <font color="Olive" title="b6">p9</font>,<font color="Olive" title="b7">q9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">c9</font>,<font color="Olive" title="b5">d9</font> implies <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b3">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">c9</font>,<font color="Olive" title="b5">d9</font> ) &amp; ( <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b3">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">c9</font>,<font color="Olive" title="b5">d9</font> implies <font color="Olive" title="b4">c9</font>,<font color="Olive" title="b5">d9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b3">b9</font> ) &amp;  ex <font color="Olive" title="b8">x9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">IT</font> st <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b3">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">c9</font>,<font color="Olive" title="b8">x9</font> ) );<br/></span></div>
