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<span class="kw">let </span><font color="Maroon" title="c3">P</font>, <font color="Maroon" title="c4">Q</font> be    <a href="pcs_0.html#L1" title="PCS_0:struct.1">TolStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <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 <font color="Maroon" title="c3">P</font>, the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c3">P</font> #) <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 <font color="Maroon" title="c4">Q</font>, the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c4">Q</font> #) &amp; <font color="Maroon" title="c3">P</font> is  <a href="pcs_0.html#V5" title="PCS_0:attr.5">pcs-tol-irreflexive</a>  implies <font color="Maroon" title="c4">Q</font> is  <a href="pcs_0.html#V5" title="PCS_0:attr.5">pcs-tol-irreflexive</a>  )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:65"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
 <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 <font color="Maroon" title="c3">P</font>, the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c3">P</font> #) <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 <font color="Maroon" title="c4">Q</font>, the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c4">Q</font> #)
 <span class="kw">and </span><br/><a NAME="E2:65"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
 the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c3">P</font> <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 <font color="Maroon" title="c3">P</font>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="pcs_0.html#D10" target="_self" title="PCS_0:def.10">PCS_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">Q</font> is  <a href="pcs_0.html#V5" title="PCS_0:attr.5">pcs-tol-irreflexive</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="relat_2.html#D2" title="RELAT_2:def.2">RELAT_2:def 2</a>,<a class="ref" href="pcs_0.html#D10" target="_self" title="PCS_0:def.10">PCS_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  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 <font color="Maroon" title="c4">Q</font> 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 <font color="Maroon" title="c4">Q</font> )</span><br/>

<span class="kw">assume </span><a NAME="E3:65"/>
<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 <font color="Maroon" title="c4">Q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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 <font color="Maroon" title="c4">Q</font></span><br/>

<span class="kw">hence </span><a NAME="E4:65"/>
 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 <font color="Maroon" title="c4">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E2:65"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="relat_2.html#D2" title="RELAT_2:def.2">RELAT_2:def 2</a></span>; <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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