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<b>let </b><font color="Maroon" title="c1">D</font>, <font color="Maroon" title="c2">C</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <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"> for <font color="Olive" title="b1">F</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">D</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <br/> for <font color="Olive" title="b2">A</font> being  <a href="rearran1.html#NM1" title="REARRAN1:NM.1">RearrangmentGen</a> of <font color="Maroon" title="c2">C</font>  st <font color="Olive" title="b1">F</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp;  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">D</font> holds <br/>(  <a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">A</font>, <a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">A</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a>  &amp;  <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p1">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">A</font></span>)</span>,<font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">A</font></span>)</span>,<font color="Maroon" title="c2">C</font> &amp;  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">A</font></span>)</span>,<font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">A</font></span>)</span>,<font color="Maroon" title="c2">C</font> )</span><br/><b>let </b><font color="Maroon" title="c3">F</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">D</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="rearran1.html#NM1" title="REARRAN1:NM.1">RearrangmentGen</a> of <font color="Maroon" title="c2">C</font>  st <font color="Maroon" title="c3">F</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp;  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">D</font> holds <br/>(  <a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Olive" title="b1">A</font>, <a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Olive" title="b1">A</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a>  &amp;  <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p1">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Olive" title="b1">A</font></span>)</span>,<font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Olive" title="b1">A</font></span>)</span>,<font color="Maroon" title="c2">C</font> &amp;  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Olive" title="b1">A</font></span>)</span>,<font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Olive" title="b1">A</font></span>)</span>,<font color="Maroon" title="c2">C</font> )</span><br/><b>let </b><font color="Maroon" title="c4">B</font> be   <a href="rearran1.html#NM1" title="REARRAN1:NM.1">RearrangmentGen</a> of <font color="Maroon" title="c2">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">F</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp;  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">D</font> implies (  <a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font>, <a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a>  &amp;  <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p1">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c2">C</font> &amp;  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c2">C</font> ) )</span><br/>







<b>assume </b><a NAME="E1:40"/>
( <font color="Maroon" title="c3">F</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp;  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">D</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font>, <a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a>  &amp;  <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p1">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c2">C</font> &amp;  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c2">C</font> )</span><br/>

<a NAME="E2:40"/><b>then </b>
(  <a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font>, <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a>  &amp;  <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font> &amp;  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font> &amp;  <a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font>, <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a>  &amp;  <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p1">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font> &amp;  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font> )
 
<b>by </b><i><a class="ref" href="rearran1.html#T17" target="_self" title="REARRAN1:th.17">Th17</a>, <a class="ref" href="rearran1.html#T18" target="_self" title="REARRAN1:th.18">Th18</a>, <a class="ref" href="rearran1.html#T19" target="_self" title="REARRAN1:th.19">Th19</a>, <a class="ref" href="rearran1.html#T24" target="_self" title="REARRAN1:th.24">Th24</a>, <a class="ref" href="rearran1.html#T25" target="_self" title="REARRAN1:th.25">Th25</a>, <a class="ref" href="rearran1.html#T26" target="_self" title="REARRAN1:th.26">Th26</a></i>;<br/>
<b>hence </b><a NAME="E3:40"/>
(  <a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font>, <a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a>  &amp;  <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p1">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c2">C</font> &amp;  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c2">C</font> )
 <b>by </b><i><a class="ref" href="rfinseq.html#T2" title="RFINSEQ:th.2">RFINSEQ:2</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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