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<span class="kw">let </span><font color="Maroon" title="c3">P</font> be    <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">D</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</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#K26" title="PCS_0:func.26">pcs-general-power</a> <font color="Maroon" title="c3">P</font>,<font color="Olive" title="b1">D</font></span>)</span>  st <font color="Olive" title="b2">p</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b3">q</font> holds <br/>for <font color="Olive" title="b4">p9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">P</font>  st <font color="Olive" title="b4">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">p</font> holds <br/> ex <font color="Olive" title="b5">q9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">P</font> st <br/>( <font color="Olive" title="b5">q9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">q</font> &amp; <font color="Olive" title="b4">p9</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b5">q9</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">D</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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 <span class="p1">(<span class="default"><a href="pcs_0.html#K26" title="PCS_0:func.26">pcs-general-power</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">D</font></span>)</span>  st <font color="Olive" title="b1">p</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b2">q</font> holds <br/>for <font color="Olive" title="b3">p9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">P</font>  st <font color="Olive" title="b3">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">p</font> holds <br/> ex <font color="Olive" title="b4">q9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">P</font> st <br/>( <font color="Olive" title="b4">q9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">q</font> &amp; <font color="Olive" title="b3">p9</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b4">q9</font> )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c5">R</font> =  <a href="pcs_0.html#K26" title="PCS_0:func.26">pcs-general-power</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">D</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c6">p</font>, <font color="Maroon" title="c7">q</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#K26" title="PCS_0:func.26">pcs-general-power</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">D</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="c6">p</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c7">q</font> implies for <font color="Olive" title="b1">p9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">P</font>  st <font color="Olive" title="b1">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">p</font> holds <br/> ex <font color="Olive" title="b2">q9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">P</font> st <br/>( <font color="Olive" title="b2">q9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">q</font> &amp; <font color="Olive" title="b1">p9</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b2">q9</font> ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:205"/><span class="lab"><font color="Green" title="E69">A1</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</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="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K26" title="PCS_0:func.26">pcs-general-power</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">D</font></span>)</span>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</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">p9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">P</font>  st <font color="Olive" title="b1">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">p</font> holds <br/> ex <font color="Olive" title="b2">q9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">P</font> st <br/>( <font color="Olive" title="b2">q9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">q</font> &amp; <font color="Olive" title="b1">p9</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b2">q9</font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c8">p9</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"> ( <font color="Maroon" title="c8">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">p</font> implies  ex <font color="Olive" title="b1">q9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">P</font> st <br/>( <font color="Olive" title="b1">q9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">q</font> &amp; <font color="Maroon" title="c8">p9</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b1">q9</font> ) )</span><br/>

<span class="kw">assume </span><a NAME="E2:205"/>
<font color="Maroon" title="c8">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">q9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">P</font> st <br/>( <font color="Olive" title="b1">q9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">q</font> &amp; <font color="Maroon" title="c8">p9</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b1">q9</font> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E4:205"/><span class="lab"><font color="Green" title="E70">A2</font></span>: 
<font color="Maroon" title="c9">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">q</font>
 <span class="kw">and </span><br/><a NAME="E5:205"/><span class="lab"><font color="Green" title="E71">A3</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">p9</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="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:205"><span class="lab"><font color="Green" title="E69">A1</font></span></a>, <a class="ref" href="pcs_0.html#D45" target="_self" title="PCS_0:def.45">Def45</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">b</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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:205"><span class="lab"><font color="Green" title="E71">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c10">b</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="c10">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">q</font> &amp; <font color="Maroon" title="c8">p9</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c10">b</font> )</span><br/>

<span class="kw">thus </span><a NAME="E7:205"/>
( <font color="Maroon" title="c10">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">q</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">p9</font>,<font color="Maroon" title="c10">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="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">P</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:205"><span class="lab"><font color="Green" title="E70">A2</font></span></a>, <a class="txt" href="#E5:205"><span class="lab"><font color="Green" title="E71">A3</font></span></a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</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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