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<b>set </b><font color="Maroon" title="c4">P</font> =  <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #);<br/>
<a NAME="E1:88_1_1"/><i><font color="Green" title="E30">A1</font></i>: 
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #),the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #) #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span> #),the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span> #) #)
 
;<br/>
<b>hence </b><a NAME="E2:88_1_1"/>
 <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #) is <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>
 <b>by </b><i><a class="ref" href="waybel_8.html#T12" title="WAYBEL_8:th.12">WAYBEL_8:12</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="pcs_0.html#D24" target="_self" title="PCS_0:def.24">PCS_0:def 24</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #) is <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a> &amp;  <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #) is <a href="pcs_0.html#V5" title="PCS_0:attr.5">pcs-tol-irreflexive</a> &amp;  <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #) is <a href="pcs_0.html#V6" title="PCS_0:attr.6">pcs-tol-symmetric</a> &amp;  <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #) is <a href="pcs_0.html#V13" title="PCS_0:attr.13">pcs-compatible</a> )</span><br/>

<b>thus </b><a NAME="E3:88_1_1"/>
 <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #) is <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>
 <b>by </b><i><a class="txt" href="pcs_0.html#E1:88_1_1"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="waybel_8.html#T13" title="WAYBEL_8:th.13">WAYBEL_8:13</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #) is <a href="pcs_0.html#V5" title="PCS_0:attr.5">pcs-tol-irreflexive</a> &amp;  <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #) is <a href="pcs_0.html#V6" title="PCS_0:attr.6">pcs-tol-symmetric</a> &amp;  <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #) is <a href="pcs_0.html#V13" title="PCS_0:attr.13">pcs-compatible</a> )</span><br/>

<a NAME="E4:88_1_1"/><i><font color="Green" title="E31">A2</font></i>: 
 <a href="pcs_0.html#G1" title="PCS_0:aggr.1">TolStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #),the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #) #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pcs_0.html#G1" title="PCS_0:aggr.1">TolStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="pcs_0.html#G1" title="PCS_0:aggr.1">TolStr</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #),the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <a href="pcs_0.html#G1" title="PCS_0:aggr.1">TolStr</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #) #)
 
;<br/>
<b>hence </b><a NAME="E5:88_1_1"/>
 <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #) is <a href="pcs_0.html#V5" title="PCS_0:attr.5">pcs-tol-irreflexive</a>
 <b>by </b><i><a class="ref" href="pcs_0.html#T4" target="_self" title="PCS_0:th.4">Th4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #) is <a href="pcs_0.html#V6" title="PCS_0:attr.6">pcs-tol-symmetric</a> &amp;  <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #) is <a href="pcs_0.html#V13" title="PCS_0:attr.13">pcs-compatible</a> )</span><br/>

<b>thus </b><a NAME="E6:88_1_1"/>
 <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #) is <a href="pcs_0.html#V6" title="PCS_0:attr.6">pcs-tol-symmetric</a>
 <b>by </b><i><a class="txt" href="pcs_0.html#E4:88_1_1"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="pcs_0.html#T5" target="_self" title="PCS_0:th.5">Th5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #) is <a href="pcs_0.html#V13" title="PCS_0:attr.13">pcs-compatible</a></span><br/>

<b>let </b><font color="Maroon" title="c5">p</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #); <i><font color="Red">:: according to </font></i><a class="ref" href="pcs_0.html#D22" target="_self" title="PCS_0:def.22">PCS_0:def 22</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p'</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">q'</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #)  st <font color="Maroon" title="c5">p</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Olive" title="b2">q</font> &amp; <font color="Olive" title="b1">p'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c5">p</font> &amp; <font color="Olive" title="b3">q'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b2">q</font> holds <br/><font color="Olive" title="b1">p'</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Olive" title="b3">q'</font></span><br/>

<b>thus </b><a NAME="E7:88_1_1"/>
for <font color="Olive" title="b1">p'</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">q'</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <font color="Maroon" title="c3">D</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c3">D</font></span>)</span>,<span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span>)</span> #)  st <font color="Maroon" title="c5">p</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Olive" title="b2">q</font> &amp; <font color="Olive" title="b1">p'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c5">p</font> &amp; <font color="Olive" title="b3">q'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b2">q</font> holds <br/><font color="Olive" title="b1">p'</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Olive" title="b3">q'</font>
 <b>by </b><i><a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></i>; <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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