<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon" title="c5">R</font> =  <a href="pcs_0.html#NK34" title="PCS_0:NK.34">pcs-general-power</a> <font color="Maroon" title="c4">D</font>;<br/>
<b>let </b><font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c7">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="c6">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 <span class="p1">(<span class="default"><a href="pcs_0.html#NK34" title="PCS_0:NK.34">pcs-general-power</a> <font color="Maroon" title="c4">D</font></span>)</span> or  not <font color="Maroon" title="c7">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 <span class="p1">(<span class="default"><a href="pcs_0.html#NK34" title="PCS_0:NK.34">pcs-general-power</a> <font color="Maroon" title="c4">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 <span class="p1">(<span class="default"><a href="pcs_0.html#NK34" title="PCS_0:NK.34">pcs-general-power</a> <font color="Maroon" title="c4">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 <span class="p1">(<span class="default"><a href="pcs_0.html#NK34" title="PCS_0:NK.34">pcs-general-power</a> <font color="Maroon" title="c4">D</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:214_1_1"/><i><font color="Green" title="E70">A1</font></i>: 
<font color="Maroon" title="c6">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 <span class="p1">(<span class="default"><a href="pcs_0.html#NK34" title="PCS_0:NK.34">pcs-general-power</a> <font color="Maroon" title="c4">D</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c7">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 <span class="p1">(<span class="default"><a href="pcs_0.html#NK34" title="PCS_0:NK.34">pcs-general-power</a> <font color="Maroon" title="c4">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 <span class="p1">(<span class="default"><a href="pcs_0.html#NK34" title="PCS_0:NK.34">pcs-general-power</a> <font color="Maroon" title="c4">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 <span class="p1">(<span class="default"><a href="pcs_0.html#NK34" title="PCS_0:NK.34">pcs-general-power</a> <font color="Maroon" title="c4">D</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E2:214_1_1"/><i><font color="Green" title="E71">A2</font></i>: 
<font color="Maroon" title="c7">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 <span class="p1">(<span class="default"><a href="pcs_0.html#NK34" title="PCS_0:NK.34">pcs-general-power</a> <font color="Maroon" title="c4">D</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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 <span class="p1">(<span class="default"><a href="pcs_0.html#NK34" title="PCS_0:NK.34">pcs-general-power</a> <font color="Maroon" title="c4">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 <span class="p1">(<span class="default"><a href="pcs_0.html#NK34" title="PCS_0:NK.34">pcs-general-power</a> <font color="Maroon" title="c4">D</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E3:214_1_1"/><i><font color="Green" title="E72">A3</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</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#NK34" title="PCS_0:NK.34">pcs-general-power</a> <font color="Maroon" title="c4">D</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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 <span class="p1">(<span class="default"><a href="pcs_0.html#NK34" title="PCS_0:NK.34">pcs-general-power</a> <font color="Maroon" title="c4">D</font></span>)</span></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="214_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c9">b</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">y</font> &amp; <font color="Maroon" title="c9">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">x</font> implies <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</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><br/><b>assume </b><a NAME="E1:214_1_1_1"/><i><font color="Green" title="E73">A4</font></i>: 
( <font color="Maroon" title="c8">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">y</font> &amp; <font color="Maroon" title="c9">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">x</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</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><br/><b>reconsider </b><font color="Maroon" title="c10">a1</font> = <font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c11">b1</font> = <font color="Maroon" title="c9">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">P</font> <b>by </b><i><a class="txt" href="#E1:214_1_1"><i><font color="Green" title="E70">A1</font></i></a>, <a class="txt" href="#E2:214_1_1"><i><font color="Green" title="E71">A2</font></i></a>, <a class="txt" href="#E1:214_1_1_1"><i><font color="Green" title="E73">A4</font></i></a></i>;<br/><a NAME="E3:214_1_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c8">a</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</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>
 <b>by </b><i><a class="txt" href="#E3:214_1_1"><i><font color="Green" title="E72">A3</font></i></a>, <a class="txt" href="#E1:214_1_1_1"><i><font color="Green" title="E73">A4</font></i></a>, <a class="ref" href="pcs_0.html#D46" target="_self" title="PCS_0:def.46">Def46</a></i>;<br/><a NAME="E4:214_1_1_1"/><b>then </b>
<font color="Maroon" title="c11">b1</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c10">a1</font>
 <b>by </b><i><a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></i>;<br/><b>hence </b><a NAME="E5:214_1_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</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>
 <b>by </b><i><a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:214_1_1"/>
<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 <span class="p1">(<span class="default"><a href="pcs_0.html#NK34" title="PCS_0:NK.34">pcs-general-power</a> <font color="Maroon" title="c4">D</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:214_1_1"><i><font color="Green" title="E70">A1</font></i></a>, <a class="txt" href="#E2:214_1_1"><i><font color="Green" title="E71">A2</font></i></a>, <a class="ref" href="pcs_0.html#D46" target="_self" title="PCS_0:def.46">Def46</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
