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<span class="kw">set </span><font color="Maroon" title="c1">F</font> =  the   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/>
<a NAME="E1:42_1_1"/>
 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>, <font color="Olive" title="b7">r</font>, <font color="Olive" title="b8">s</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="parsp_1.html#K9" title="PARSP_1:func.9">MPS</a>  the   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a></span>)</span> holds <br/> ( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</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="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b3">c</font> &amp; ( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b7">r</font>,<font color="Olive" title="b8">s</font> &amp;  not <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b7">r</font>,<font color="Olive" title="b8">s</font> implies <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> ) &amp; ( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> implies <font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> ) &amp;  ex <font color="Olive" title="b9">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="parsp_1.html#K9" title="PARSP_1:func.9">MPS</a>  the   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a></span>)</span> st <br/>( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b9">x</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b9">x</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="parsp_1.html#T13" target="_self" title="PARSP_1:th.13">Th24</a>, <a class="ref" href="parsp_1.html#T14" target="_self" title="PARSP_1:th.14">Th25</a>, <a class="ref" href="parsp_1.html#T15" target="_self" title="PARSP_1:th.15">Th26</a>, <a class="ref" href="parsp_1.html#T16" target="_self" title="PARSP_1:th.16">Th27</a>, <a class="ref" href="parsp_1.html#T17" target="_self" title="PARSP_1:th.17">Th28</a></span>;<br/>
<a NAME="E2:42_1_1"/><span class="kw">then </span>
 <a href="parsp_1.html#K9" title="PARSP_1:func.9">MPS</a>  the   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a> is  <a href="parsp_1.html#V2" title="PARSP_1:attr.2">ParSp-like</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="parsp_1.html#D12" target="_self" title="PARSP_1:def.12">Def12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:42_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="parsp_1.html#L1" title="PARSP_1:struct.1">ParStr</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> is  <a href="parsp_1.html#V1" title="PARSP_1:attr.1">strict</a>  &amp; <font color="Olive">b<sub>1</sub></font> is  <a href="parsp_1.html#V2" title="PARSP_1:attr.2">ParSp-like</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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