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<b>set </b><font color="Maroon" title="c4">P</font> =  <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>thus </b><a NAME="E1:42_1_1"/>
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> #) <a href="relat_2.html#R2" title="RELAT_2:pred.2">is_irreflexive_in</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> #)
  <i><font color="Red">:: according to </font></i><a class="ref" href="pcs_0.html#D10" target="_self" title="PCS_0:def.10">PCS_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_2.html#D2" title="RELAT_2:def.2">RELAT_2:def 2</a><br/>

<b>thus </b><a NAME="E1:42_1_1_1"/>
(  not <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> #) or  not <span class="p1"><a href="pcs_0.html#NK13" title="PCS_0:NK.13">[^</a><span class="default">,</span><a href="pcs_0.html#NK13" title="PCS_0:NK.13">^]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 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/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_2.html#D3" title="RELAT_2:def.3">RELAT_2:def 3</a>,<a class="ref" href="pcs_0.html#D11" target="_self" title="PCS_0:def.11">PCS_0:def 11</a><br/>

<b>thus </b><a NAME="E2:42_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> #) or  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> #) or  not <span class="p1"><a href="pcs_0.html#NK13" title="PCS_0:NK.13">[^</a><span class="default">,</span><a href="pcs_0.html#NK13" title="PCS_0:NK.13">^]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 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> #) or <span class="p1"><a href="pcs_0.html#NK13" title="PCS_0:NK.13">[^</a><span class="default">,</span><a href="pcs_0.html#NK13" title="PCS_0:NK.13">^]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 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/>


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