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<b>consider </b><font color="Maroon" title="c3">OTS</font> being   <a href="geomtrap.html#NM2" title="GEOMTRAP:NM.2">OrdTrapSpace</a>;<br/>
<b>set </b><font color="Maroon" title="c4">TS</font> =  <a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c3">OTS</font>;<br/>
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for <font color="Olive" title="b1">a'</font>, <font color="Olive" title="b2">b'</font>, <font color="Olive" title="b3">c'</font>, <font color="Olive" title="b4">d'</font>, <font color="Olive" title="b5">p'</font>, <font color="Olive" title="b6">q'</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c3">OTS</font></span>)</span> holds <br/> ( <font color="Olive" title="b1">a'</font>,<font color="Olive" title="b2">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b'</font>,<font color="Olive" title="b1">a'</font> &amp; ( <font color="Olive" title="b1">a'</font>,<font color="Olive" title="b2">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c'</font>,<font color="Olive" title="b4">d'</font> &amp; <font color="Olive" title="b1">a'</font>,<font color="Olive" title="b2">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c'</font>,<font color="Olive" title="b6">q'</font> &amp; not <font color="Olive" title="b1">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b'</font> implies <font color="Olive" title="b4">d'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">q'</font> ) &amp; ( <font color="Olive" title="b5">p'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">q'</font> &amp; <font color="Olive" title="b5">p'</font>,<font color="Olive" title="b6">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a'</font>,<font color="Olive" title="b2">b'</font> &amp; <font color="Olive" title="b5">p'</font>,<font color="Olive" title="b6">q'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c'</font>,<font color="Olive" title="b4">d'</font> implies <font color="Olive" title="b1">a'</font>,<font color="Olive" title="b2">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c'</font>,<font color="Olive" title="b4">d'</font> ) &amp; ( <font color="Olive" title="b1">a'</font>,<font color="Olive" title="b2">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c'</font>,<font color="Olive" title="b4">d'</font> implies <font color="Olive" title="b3">c'</font>,<font color="Olive" title="b4">d'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a'</font>,<font color="Olive" title="b2">b'</font> ) &amp;  ex <font color="Olive" title="b7">x'</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c3">OTS</font></span>)</span> st <font color="Olive" title="b1">a'</font>,<font color="Olive" title="b2">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c'</font>,<font color="Olive" title="b7">x'</font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E103"><i><font color="Green" title="E86">Lm36</font></i></a>, <a class="txt" href="geomtrap.html#E104"><i><font color="Green" title="E87">Lm37</font></i></a>, <a class="txt" href="geomtrap.html#E105"><i><font color="Green" title="E88">Lm38</font></i></a>, <a class="txt" href="geomtrap.html#E106"><i><font color="Green" title="E89">Lm39</font></i></a>, <a class="txt" href="geomtrap.html#E108"><i><font color="Green" title="E91">Lm41</font></i></a></i>;<br/>
<a NAME="E3:111_1_1"/><b>then </b>
 <a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c3">OTS</font> is <a href="geomtrap.html#V4" title="GEOMTRAP:attr.4">TrapSpace-like</a>
 
<b>by </b><i><a class="ref" href="geomtrap.html#D15" target="_self" title="GEOMTRAP:def.15">Def15</a></i>;<br/>
<b>hence </b><a NAME="E4:111_1_1"/>
 ex <font color="Olive">b<sub>1</sub></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>  st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="analoaf.html#V1" title="ANALOAF:attr.1">strict</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="geomtrap.html#V4" title="GEOMTRAP:attr.4">TrapSpace-like</a> )
 ; <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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