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<b>let </b><font color="Maroon" title="c1">f</font>, <font color="Maroon" title="c2">g</font>, <font color="Maroon" title="c3">h</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  iff <font color="Maroon" title="c1">f</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font>,<font color="Maroon" title="c2">g</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  )</span><br/>

<b>thus </b><a NAME="E1:2"/>
( <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  implies <font color="Maroon" title="c1">f</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font>,<font color="Maroon" title="c2">g</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">f</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font>,<font color="Maroon" title="c2">g</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  implies <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:2_1"/><i><font color="Green" title="E2">A1</font></i>: 
<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">f</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font>,<font color="Maroon" title="c2">g</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">y</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">  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font></span>)</span>,<font color="Maroon" title="c4">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font></span>)</span>,<font color="Maroon" title="c4">y</font></span>)</span></span><br/><a NAME="E1:2_1_1"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c4">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c4">y</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:2_1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="classes1.html#D9" title="CLASSES1:def.9">CLASSES1:def 9</a></i>;<br/><b>hence </b> <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font></span>)</span>,<font color="Maroon" title="c4">y</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c4">y</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <font color="Maroon" title="c3">h</font>,<font color="Maroon" title="c4">y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_3.html#T63" title="FINSEQ_3:th.63">FINSEQ_3:63</a></i>
<br/>.= 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font></span>)</span>,<font color="Maroon" title="c4">y</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_3.html#T63" title="FINSEQ_3:th.63">FINSEQ_3:63</a></i>
;<br/> <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="E3:2_1"/>
<font color="Maroon" title="c1">f</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font>,<font color="Maroon" title="c2">g</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> 
 <b>by </b><i><a class="ref" href="classes1.html#D9" title="CLASSES1:def.9">CLASSES1:def 9</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>assume </b><a NAME="E2:2"/><i><font color="Green" title="E2">A2</font></i>: 
<font color="Maroon" title="c1">f</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font>,<font color="Maroon" title="c2">g</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">x</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">  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c4">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c4">x</font></span>)</span></span><br/><a NAME="E1:2_2"/>
(  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font></span>)</span>,<font color="Maroon" title="c4">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c4">x</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <font color="Maroon" title="c3">h</font>,<font color="Maroon" title="c4">x</font></span>)</span></span>)</span> &amp;  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font></span>)</span>,<font color="Maroon" title="c4">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c4">x</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <font color="Maroon" title="c3">h</font>,<font color="Maroon" title="c4">x</font></span>)</span></span>)</span> &amp;  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font></span>)</span>,<font color="Maroon" title="c4">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">h</font></span>)</span>,<font color="Maroon" title="c4">x</font></span>)</span> )
 <b>by </b><i><a class="txt" href="#E2:2"><i><font color="Green" title="E2">A2</font></i></a>, <a class="ref" href="classes1.html#D9" title="CLASSES1:def.9">CLASSES1:def 9</a>, <a class="ref" href="finseq_3.html#T63" title="FINSEQ_3:th.63">FINSEQ_3:63</a></i>;<br/><b>hence </b><a NAME="E2:2_2"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c4">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K12" title="RELAT_1:func.12">Coim</a> <font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c4">x</font></span>)</span>
 ; <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="E4:2"/>
<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> 
 <b>by </b><i><a class="ref" href="classes1.html#D9" title="CLASSES1:def.9">CLASSES1:def 9</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>
