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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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#V6" title="PCS_0:attr.6">pcs-tol-symmetric</a> implies <font color="Maroon" title="c4">Q</font> is <a href="pcs_0.html#V6" title="PCS_0:attr.6">pcs-tol-symmetric</a> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:67"/><i><font color="Green" title="E25">A1</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 <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> #)
 <b>and </b><br/><a NAME="E2:67"/><i><font color="Green" title="E26">A2</font></i>: 
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#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 <font color="Maroon" title="c3">P</font>
 ; <i><font color="Red">:: according to </font></i><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">Q</font> is <a href="pcs_0.html#V6" title="PCS_0:attr.6">pcs-tol-symmetric</a></span><br/>

<b>let </b><font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c6">y</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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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 <font color="Maroon" title="c6">y</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> 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 <font color="Maroon" title="c4">Q</font> )</span><br/>

<b>assume </b><a NAME="E3:67"/>
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c6">y</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> 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 <font color="Maroon" title="c4">Q</font> )</span><br/>

<b>hence </b><a NAME="E4:67"/>
(  not <font color="Maroon" title="c6">y</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> 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 <font color="Maroon" title="c4">Q</font> )
 <b>by </b><i><a class="txt" href="pcs_0.html#E1:67"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="pcs_0.html#E2:67"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="relat_2.html#D3" title="RELAT_2:def.3">RELAT_2:def 3</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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