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<span class="kw">let </span><font color="Maroon" title="c3">P</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pcs_0.html#L2" title="PCS_0:struct.2">pcs-Str</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">P</font><br/> for <font color="Olive" title="b3">p9</font>, <font color="Olive" title="b4">q9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</font></span>)</span>  st <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">p9</font> &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">q9</font> &amp; not <font color="Olive" title="b3">p9</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Olive" title="b4">q9</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="b2">q</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">p</font>, <font color="Maroon" title="c5">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">P</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p9</font>, <font color="Olive" title="b2">q9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</font></span>)</span>  st <font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p9</font> &amp; <font color="Maroon" title="c5">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q9</font> &amp; not <font color="Olive" title="b1">p9</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Olive" title="b2">q9</font> holds <br/><font color="Maroon" title="c4">p</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c5">q</font></span><br/>



<span class="kw">set </span><font color="Maroon" title="c6">R</font> =  <a href="pcs_0.html#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c7">p9</font>, <font color="Maroon" title="c8">q9</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">p9</font> &amp; <font color="Maroon" title="c5">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q9</font> &amp; not <font color="Maroon" title="c7">p9</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c8">q9</font> implies <font color="Maroon" title="c4">p</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c5">q</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:162"/><span class="lab"><font color="Green" title="E63">A1</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">p9</font>
 <span class="kw">and </span><br/><a NAME="E2:162"/><span class="lab"><font color="Green" title="E64">A2</font></span>: 
<font color="Maroon" title="c5">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">p9</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c8">q9</font> or <font color="Maroon" title="c4">p</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c5">q</font> )</span><br/>

<a NAME="E3:162"/><span class="lab"><font color="Green" title="E65">A3</font></span>: 
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#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c3">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#D40" target="_self" title="PCS_0:def.40">Def40</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:162"/><span class="lab"><font color="Green" title="E66">A4</font></span>: 
not <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c7">p9</font>,<font color="Maroon" title="c8">q9</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</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 <span class="p1">(<span class="default"><a href="pcs_0.html#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</font></span>)</span>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">PCS_0:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">p</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c5">q</font></span><br/>

<a NAME="E5:162"/>
<span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">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="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">P</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:162"/>
<span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</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="c3">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:162"><span class="lab"><font color="Green" title="E63">A1</font></span></a>, <a class="txt" href="#E2:162"><span class="lab"><font color="Green" title="E64">A2</font></span></a>, <a class="txt" href="#E3:162"><span class="lab"><font color="Green" title="E65">A3</font></span></a>, <a class="txt" href="#E4:162"><span class="lab"><font color="Green" title="E66">A4</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">PCS_0:def 7</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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