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<span class="kw">let </span><font color="Maroon" title="c1">r</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</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>, <font color="Olive" title="b2">C</font> being 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> <br/> for <font color="Olive" title="b3">F</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Olive" title="b1">D</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <br/> for <font color="Olive" title="b4">A</font> being  <a href="rearran1.html#NM1" title="REARRAN1:NM.1">RearrangmentGen</a> of <font color="Olive" title="b2">C</font>  st <font color="Olive" title="b3">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="Olive" title="b2">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="Olive" title="b1">D</font> holds <br/>(  <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Olive" title="b3">F</font>,<font color="Olive" title="b4">A</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span>, <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span> <a href="classes1.html#R2" title="CLASSES1:pred.2">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Olive" title="b3">F</font>,<font color="Olive" title="b4">A</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Olive" title="b2">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Olive" title="b1">D</font> &amp;  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Olive" title="b3">F</font>,<font color="Olive" title="b4">A</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Olive" title="b2">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Olive" title="b1">D</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">D</font>, <font color="Maroon" title="c3">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c2">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="c3">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="c3">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="c2">D</font> holds <br/>(  <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span>, <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span> <a href="classes1.html#R2" title="CLASSES1:pred.2">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<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> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">D</font> &amp;  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<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> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">D</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">F</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c2">D</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</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">A</font> being  <a href="rearran1.html#NM1" title="REARRAN1:NM.1">RearrangmentGen</a> of <font color="Maroon" title="c3">C</font>  st <font color="Maroon" title="c4">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="c3">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="c2">D</font> holds <br/>(  <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Olive" title="b1">A</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span>, <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span> <a href="classes1.html#R2" title="CLASSES1:pred.2">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Olive" title="b1">A</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">D</font> &amp;  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Olive" title="b1">A</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">D</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">B</font> be   <a href="rearran1.html#NM1" title="REARRAN1:NM.1">RearrangmentGen</a> of <font color="Maroon" title="c3">C</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="c4">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="c3">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="c2">D</font> implies (  <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span>, <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span> <a href="classes1.html#R2" title="CLASSES1:pred.2">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">D</font> &amp;  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">D</font> ) )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:47"/><span class="lab"><font color="Green" title="E34">A1</font></span>: 
<font color="Maroon" title="c4">F</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> 
 <span class="kw">and </span><br/><a NAME="E2:47"/><span class="lab"><font color="Green" title="E35">A2</font></span>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">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="c2">D</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span>, <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span> <a href="classes1.html#R2" title="CLASSES1:pred.2">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">D</font> &amp;  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">D</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">mp</font> =  <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">mf</font> =  <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span>;<br/>
<a NAME="E3:47"/><span class="lab"><font color="Green" title="E36">A3</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<a NAME="E4:47"/><span class="kw">then </span>
<font color="Maroon" title="c4">F</font> <a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">|</a> <font color="Maroon" title="c2">D</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c4">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T97" title="RELAT_1:th.97">RELAT_1:97</a></span>;<br/>
<a NAME="E5:47"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A4</font></span>: 
 <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c4">F</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:47"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="ref" href="rfunct_3.html#D14" title="RFUNCT_3:def.14">RFUNCT_3:def 14</a></span>;<br/>
<a NAME="E6:47"/>
 <a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font>, <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="txt" href="#E2:47"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="ref" href="rearran1.html#T24" target="_self" title="REARRAN1:th.24">Th24</a></span>;<br/>
<a NAME="E7:47"/><span class="kw">then </span>
 <a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c4">F</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="ref" href="classes1.html#T84" title="CLASSES1:th.84">CLASSES1:84</a></span>;<br/>
<a NAME="E8:47"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_3.html#T54" title="RFUNCT_3:th.54">RFUNCT_3:54</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:47"/><span class="lab"><font color="Green" title="E38">A5</font></span>: 
 <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span>, <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_3.html#T45" title="RFUNCT_3:th.45">RFUNCT_3:45</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">D</font> &amp;  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">D</font> )</span><br/>

<a NAME="E10:47"/><span class="lab"><font color="Green" title="E39">A6</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_3.html#D11" title="RFUNCT_3:def.11">RFUNCT_3:def 11</a></span>;<br/>
<a NAME="E11:47"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">|</a> <font color="Maroon" title="c3">C</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T97" title="RELAT_1:th.97">RELAT_1:97</a></span>;<br/>
<a NAME="E12:47"/><span class="kw">then </span>
 <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">C</font>, <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:47"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="ref" href="rfunct_3.html#D14" title="RFUNCT_3:def.14">RFUNCT_3:def 14</a></span>;<br/>
<a NAME="E13:47"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A7</font></span>: 
 <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">C</font>, <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:47"><span class="lab"><font color="Green" title="E38">A5</font></span></a>, <a class="ref" href="classes1.html#T84" title="CLASSES1:th.84">CLASSES1:84</a></span>;<br/>
<a NAME="E14:47"/><span class="lab"><font color="Green" title="E41">A8</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_3.html#D11" title="RFUNCT_3:def.11">RFUNCT_3:def 11</a></span>;<br/>
<a NAME="E15:47"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">|</a> <font color="Maroon" title="c2">D</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T97" title="RELAT_1:th.97">RELAT_1:97</a></span>;<br/>
<span class="kw">hence </span><a NAME="E16:47"/>
 <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">D</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:47"><span class="lab"><font color="Green" title="E41">A8</font></span></a>, <a class="txt" href="#E13:47"><span class="lab"><font color="Green" title="E40">A7</font></span></a>, <a class="ref" href="rfunct_3.html#D14" title="RFUNCT_3:def.14">RFUNCT_3:def 14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">D</font></span><br/>

<span class="kw">hence </span> <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">C</font> = 
 <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">D</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_3.html#D15" title="RFUNCT_3:def.15">RFUNCT_3:def 15</a></span>
<br/>.= 
 <a href="rfunct_3.html#K23" title="RFUNCT_3:func.23">Sum</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="valued_1.html#K15" title="VALUED_1:func.15">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">D</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_3.html#D15" title="RFUNCT_3:def.15">RFUNCT_3:def 15</a></span>
;<br/> <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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