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<span class="kw">set </span><font color="Maroon" title="c4">P</font> =  <a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">IR</font> = the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">TR</font> = the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font></span>)</span>;<br/>
<a NAME="E1:85_1_1"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
 <a href="pcs_0.html#K1" title="PCS_0:func.1">field</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="orders_1.html#T97" title="ORDERS_1:th.97">ORDERS_1:97</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:85_1_1"/>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font></span>)</span> <a href="relat_2.html#R1" title="RELAT_2:pred.1">is_reflexive_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_2.html#D9" title="RELAT_2:def.9">RELAT_2:def 9</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="orders_2.html#D4" title="ORDERS_2:def.4">ORDERS_2:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font> is  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>  &amp;  <a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font> is  <a href="pcs_0.html#V4" title="PCS_0:attr.4">pcs-tol-reflexive</a>  &amp;  <a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font> is  <a href="pcs_0.html#V6" title="PCS_0:attr.6">pcs-tol-symmetric</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E3:85_1_1"/>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font></span>)</span> <a href="relat_2.html#R8" title="RELAT_2:pred.8">is_transitive_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:85_1_1"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="relat_2.html#D16" title="RELAT_2:def.16">RELAT_2:def 16</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font> is  <a href="pcs_0.html#V4" title="PCS_0:attr.4">pcs-tol-reflexive</a>  &amp;  <a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font> is  <a href="pcs_0.html#V6" title="PCS_0:attr.6">pcs-tol-symmetric</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E4:85_1_1"/>
the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font></span>)</span> <a href="relat_2.html#R1" title="RELAT_2:pred.1">is_reflexive_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:85_1_1"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="relat_2.html#D9" title="RELAT_2:def.9">RELAT_2:def 9</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="pcs_0.html#D9" target="_self" title="PCS_0:def.9">PCS_0:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font> is  <a href="pcs_0.html#V6" title="PCS_0:attr.6">pcs-tol-symmetric</a> </span><br/>

<span class="kw">thus </span><a NAME="E5:85_1_1"/>
the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font></span>)</span> <a href="relat_2.html#R3" title="RELAT_2:pred.3">is_symmetric_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:85_1_1"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="relat_2.html#D11" title="RELAT_2:def.11">RELAT_2:def 11</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="pcs_0.html#D11" target="_self" title="PCS_0:def.11">PCS_0:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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