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

<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being   <a href="valued_0.html#V6" title="VALUED_0:attr.6">natural-valued</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 holds <br/>( <font color="Olive" title="b1">f1</font>,<font color="Olive" title="b2">f2</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  iff <font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Olive" title="b1">f1</font>,<font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Olive" title="b2">f2</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">f1</font>, <font color="Maroon" title="c3">f2</font> be   <a href="valued_0.html#V6" title="VALUED_0:attr.6">natural-valued</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 implies ( <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">f2</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  iff <font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:44"/><span class="lab"><font color="Green" title="E31">A1</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">f2</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  iff <font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c4">n1</font> = <font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">n2</font> = <font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font>;<br/>
<span class="kw">thus </span><a NAME="E2:44"/>
( <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">f2</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  implies <font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  )
  <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  implies <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">f2</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="44_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:44_1"/><span class="lab"><font color="Green" title="E32">A2</font></span>: 
<font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">f2</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> </span><br/>

<a NAME="E2:44_1"/>
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds   <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>,<font color="Olive" title="b1">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>,<font color="Olive" title="b1">x</font>)</span>)</span>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="44_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>,<font color="Maroon" title="c6">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>,<font color="Maroon" title="c6">x</font>)</span>)</span></span><br/>

<a NAME="E1:44_1_1"/><span class="lab"><font color="Green" title="E33">A3</font></span>: 
(  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>,<font color="Maroon" title="c6">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>,<font color="Maroon" title="c6">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D17" onmouseover="rs('relat_1/D17')" onmouseout="rh()">RELAT_1:def 17</a></span>;<br/>
<a NAME="E2:44_1_1"/><span class="lab"><font color="Green" title="E34">A4</font></span>: 
(  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">f1</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c3">f2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="flexary1.html#D4" target="_self" onmouseover="rs('flexary1/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:44_1_1_1"/>
( (  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> &amp;  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> ) or ( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> &amp;  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> ) or ( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> &amp;  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> ) or ( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> &amp; <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:44_1_1_1_1"/>
(  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> &amp;  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>,<font color="Maroon" title="c6">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>,<font color="Maroon" title="c6">x</font>)</span>)</span></span><br/><div class="add"><a NAME="E2:44_1_1_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T72" onmouseover="rs('funct_1/T72')" onmouseout="rh()">FUNCT_1:72</a></span>;<br/><span class="kw">hence </span><a NAME="E3:44_1_1_1_1"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>,<font color="Maroon" title="c6">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>,<font color="Maroon" title="c6">x</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44_1_1"><span class="lab"><font color="Green" title="E33">A3</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:44_1_1_1_2"/><span class="lab"><font color="Green" title="E35">A5</font></span>: 
( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> &amp;  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>,<font color="Maroon" title="c6">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>,<font color="Maroon" title="c6">x</font>)</span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:44_1_1_1_2"/><span class="lab"><font color="Green" title="E36">A6</font></span>: 
( <font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E4:44_1_1_1_2"/><span class="lab"><font color="Green" title="E37">A7</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44_1_1_1_2"><span class="lab"><font color="Green" title="E36">A6</font></span></a>, <a class="txt" href="#E2:44_1_1"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="ref" href="flexary1.html#D4" target="_self" onmouseover="rs('flexary1/D4')" onmouseout="rh()">Def4</a></span>;<br/><a NAME="E5:44_1_1_1_2"/>
<font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">f1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44_1_1_1_2"><span class="lab"><font color="Green" title="E36">A6</font></span></a>, <a class="txt" href="#E2:44_1_1"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E6:44_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">f1</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T72" onmouseover="rs('funct_1/T72')" onmouseout="rh()">FUNCT_1:72</a></span>;<br/><a NAME="E7:44_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A8</font></span>: 
 <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c2">f1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D17" onmouseover="rs('relat_1/D17')" onmouseout="rh()">RELAT_1:def 17</a></span>;<br/><a NAME="E8:44_1_1_1_2"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c2">f1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44_1"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="classes1.html#D10" onmouseover="rs('classes1/D10')" onmouseout="rh()">CLASSES1:def 10</a></span>;<br/><a NAME="E9:44_1_1_1_2"/><span class="kw">then </span>
 <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:44_1_1_1_2"><span class="lab"><font color="Green" title="E38">A8</font></span></a></span>;<br/><a NAME="E10:44_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">f2</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D17" onmouseover="rs('relat_1/D17')" onmouseout="rh()">RELAT_1:def 17</a></span>;<br/><a NAME="E11:44_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c3">f2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T72" onmouseover="rs('funct_1/T72')" onmouseout="rh()">FUNCT_1:72</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E13:44_1_1_1_2"/><span class="lab"><font color="Green" title="E39">A9</font></span>: 
( <font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c3">f2</font> &amp; <font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E14:44_1_1_1_2"/><span class="lab"><font color="Green" title="E40">A10</font></span>: 
<font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:44_1_1_1_2"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="ref" href="flexary1.html#D4" target="_self" onmouseover="rs('flexary1/D4')" onmouseout="rh()">Def4</a></span>;<br/><a NAME="E15:44_1_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:44_1_1_1_2"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="ref" href="flexary1.html#D4" target="_self" onmouseover="rs('flexary1/D4')" onmouseout="rh()">Def4</a>, <a class="txt" href="#E4:44_1_1_1_2"><span class="lab"><font color="Green" title="E37">A7</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E16:44_1_1_1_2"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>,<font color="Maroon" title="c6">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>,<font color="Maroon" title="c6">x</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:44_1_1_1_2"><span class="lab"><font color="Green" title="E40">A10</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a>, <a class="txt" href="#E1:44_1_1_1_2"><span class="lab"><font color="Green" title="E35">A5</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:44_1_1_1_3"/><span class="lab"><font color="Green" title="E35">A11</font></span>: 
( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> &amp;  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>,<font color="Maroon" title="c6">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>,<font color="Maroon" title="c6">x</font>)</span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:44_1_1_1_3"/><span class="lab"><font color="Green" title="E36">A12</font></span>: 
( <font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E4:44_1_1_1_3"/><span class="lab"><font color="Green" title="E37">A13</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44_1_1_1_3"><span class="lab"><font color="Green" title="E36">A12</font></span></a>, <a class="txt" href="#E2:44_1_1"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="ref" href="flexary1.html#D4" target="_self" onmouseover="rs('flexary1/D4')" onmouseout="rh()">Def4</a></span>;<br/><a NAME="E5:44_1_1_1_3"/>
<font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c3">f2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44_1_1_1_3"><span class="lab"><font color="Green" title="E36">A12</font></span></a>, <a class="txt" href="#E2:44_1_1"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E6:44_1_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c3">f2</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T72" onmouseover="rs('funct_1/T72')" onmouseout="rh()">FUNCT_1:72</a></span>;<br/><a NAME="E7:44_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A14</font></span>: 
 <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D17" onmouseover="rs('relat_1/D17')" onmouseout="rh()">RELAT_1:def 17</a></span>;<br/><a NAME="E8:44_1_1_1_3"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c2">f1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44_1"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="classes1.html#D10" onmouseover="rs('classes1/D10')" onmouseout="rh()">CLASSES1:def 10</a></span>;<br/><a NAME="E9:44_1_1_1_3"/><span class="kw">then </span>
 <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c2">f1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:44_1_1_1_3"><span class="lab"><font color="Green" title="E38">A14</font></span></a></span>;<br/><a NAME="E10:44_1_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c2">f1</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D17" onmouseover="rs('relat_1/D17')" onmouseout="rh()">RELAT_1:def 17</a></span>;<br/><a NAME="E11:44_1_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">f1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T72" onmouseover="rs('funct_1/T72')" onmouseout="rh()">FUNCT_1:72</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E13:44_1_1_1_3"/><span class="lab"><font color="Green" title="E39">A15</font></span>: 
( <font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E14:44_1_1_1_3"/><span class="lab"><font color="Green" title="E40">A16</font></span>: 
<font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:44_1_1_1_3"><span class="lab"><font color="Green" title="E39">A15</font></span></a>, <a class="ref" href="flexary1.html#D4" target="_self" onmouseover="rs('flexary1/D4')" onmouseout="rh()">Def4</a></span>;<br/><a NAME="E15:44_1_1_1_3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:44_1_1_1_3"><span class="lab"><font color="Green" title="E39">A15</font></span></a>, <a class="ref" href="flexary1.html#D4" target="_self" onmouseover="rs('flexary1/D4')" onmouseout="rh()">Def4</a>, <a class="txt" href="#E4:44_1_1_1_3"><span class="lab"><font color="Green" title="E37">A13</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E16:44_1_1_1_3"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>,<font color="Maroon" title="c6">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>,<font color="Maroon" title="c6">x</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:44_1_1_1_3"><span class="lab"><font color="Green" title="E40">A16</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a>, <a class="txt" href="#E1:44_1_1_1_3"><span class="lab"><font color="Green" title="E35">A11</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_1_1_4"><span class="kw">suppose </span></a><a NAME="E1:44_1_1_1_4"/><span class="lab"><font color="Green" title="E35">A17</font></span>: 
( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> &amp; <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>,<font color="Maroon" title="c6">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>,<font color="Maroon" title="c6">x</font>)</span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">y1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:44_1_1_1_4"/><span class="lab"><font color="Green" title="E36">A18</font></span>: 
( <font color="Maroon" title="c7">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E4:44_1_1_1_4"/><span class="lab"><font color="Green" title="E37">A19</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44_1_1_1_4"><span class="lab"><font color="Green" title="E36">A18</font></span></a>, <a class="txt" href="#E2:44_1_1"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="ref" href="flexary1.html#D4" target="_self" onmouseover="rs('flexary1/D4')" onmouseout="rh()">Def4</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c8">y2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E6:44_1_1_1_4"/><span class="lab"><font color="Green" title="E38">A20</font></span>: 
( <font color="Maroon" title="c8">y2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44_1_1_1_4"><span class="lab"><font color="Green" title="E35">A17</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E7:44_1_1_1_4"/><span class="lab"><font color="Green" title="E39">A21</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:44_1_1_1_4"><span class="lab"><font color="Green" title="E38">A20</font></span></a>, <a class="txt" href="#E2:44_1_1"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="ref" href="flexary1.html#D4" target="_self" onmouseover="rs('flexary1/D4')" onmouseout="rh()">Def4</a></span>;<br/><a NAME="E8:44_1_1_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A22</font></span>: 
<font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:44_1_1_1_4"><span class="lab"><font color="Green" title="E37">A19</font></span></a>, <a class="txt" href="#E1:44"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="pepin.html#T30" onmouseover="rs('pepin/T30')" onmouseout="rh()">PEPIN:30</a></span>;<br/><a NAME="E9:44_1_1_1_4"/><span class="lab"><font color="Green" title="E41">A23</font></span>: 
 <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y2</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>,<font color="Maroon" title="c6">x</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="flexary1.html#T28" target="_self" onmouseover="rs('flexary1/T28')" onmouseout="rh()">Th28</a>, <a class="txt" href="#E7:44_1_1_1_4"><span class="lab"><font color="Green" title="E39">A21</font></span></a></span>;<br/><a NAME="E10:44_1_1_1_4"/>
 <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c2">f1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y1</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>,<font color="Maroon" title="c6">x</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="flexary1.html#T28" target="_self" onmouseover="rs('flexary1/T28')" onmouseout="rh()">Th28</a>, <a class="txt" href="#E4:44_1_1_1_4"><span class="lab"><font color="Green" title="E37">A19</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E11:44_1_1_1_4"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>,<font color="Maroon" title="c6">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>,<font color="Maroon" title="c6">x</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:44_1_1_1_4"><span class="lab"><font color="Green" title="E40">A22</font></span></a>, <a class="txt" href="#E1:44_1"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="classes1.html#D10" onmouseover="rs('classes1/D10')" onmouseout="rh()">CLASSES1:def 10</a>, <a class="txt" href="#E9:44_1_1_1_4"><span class="lab"><font color="Green" title="E41">A23</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:44_1"/>
<font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</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="classes1.html#D10" onmouseover="rs('classes1/D10')" onmouseout="rh()">CLASSES1:def 10</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E3:44"/><span class="lab"><font color="Green" title="E32">A24</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">f2</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> </span><br/>

<a NAME="E4:44"/>
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds   <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c2">f1</font>,<font color="Olive" title="b1">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f2</font>,<font color="Olive" title="b1">x</font>)</span>)</span>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="44_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c6">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c6">x</font>)</span>)</span></span><br/>

<a NAME="E1:44_2"/><span class="lab"><font color="Green" title="E33">A25</font></span>: 
(  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c6">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c6">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D17" onmouseover="rs('relat_1/D17')" onmouseout="rh()">RELAT_1:def 17</a></span>;<br/>
<a NAME="E2:44_2"/><span class="lab"><font color="Green" title="E34">A26</font></span>: 
(  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">f1</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c3">f2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="flexary1.html#D4" target="_self" onmouseover="rs('flexary1/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_2_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:44_2_1"/>
( (  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">f1</font> &amp;  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c3">f2</font> ) or ( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">f1</font> &amp;  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c3">f2</font> ) or ( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c3">f2</font> &amp;  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">f1</font> ) or ( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c3">f2</font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:44_2_1_1"/>
(  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">f1</font> &amp;  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c3">f2</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c6">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c6">x</font>)</span>)</span></span><br/><div class="add"><a NAME="E2:44_2_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c2">f1</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">f2</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T72" onmouseover="rs('funct_1/T72')" onmouseout="rh()">FUNCT_1:72</a></span>;<br/><span class="kw">hence </span><a NAME="E3:44_2_1_1"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c6">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c6">x</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44_2"><span class="lab"><font color="Green" title="E33">A25</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:44_2_1_2"/><span class="lab"><font color="Green" title="E35">A27</font></span>: 
( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">f1</font> &amp;  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c3">f2</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c6">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c6">x</font>)</span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:44_2_1_2"/><span class="lab"><font color="Green" title="E36">A28</font></span>: 
( <font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E4:44_2_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:44_2"><span class="lab"><font color="Green" title="E34">A26</font></span></a>, <a class="txt" href="#E3:44_2_1_2"><span class="lab"><font color="Green" title="E36">A28</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E5:44_2_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T72" onmouseover="rs('funct_1/T72')" onmouseout="rh()">FUNCT_1:72</a></span>;<br/><a NAME="E6:44_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A29</font></span>: 
 <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D17" onmouseover="rs('relat_1/D17')" onmouseout="rh()">RELAT_1:def 17</a></span>;<br/><a NAME="E7:44_2_1_2"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44"><span class="lab"><font color="Green" title="E32">A24</font></span></a>, <a class="ref" href="classes1.html#D10" onmouseover="rs('classes1/D10')" onmouseout="rh()">CLASSES1:def 10</a></span>;<br/><a NAME="E8:44_2_1_2"/><span class="kw">then </span>
 <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:44_2_1_2"><span class="lab"><font color="Green" title="E37">A29</font></span></a></span>;<br/><a NAME="E9:44_2_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D17" onmouseover="rs('relat_1/D17')" onmouseout="rh()">RELAT_1:def 17</a></span>;<br/><a NAME="E10:44_2_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T72" onmouseover="rs('funct_1/T72')" onmouseout="rh()">FUNCT_1:72</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E12:44_2_1_2"/><span class="lab"><font color="Green" title="E38">A30</font></span>: 
( <font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E13:44_2_1_2"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">z</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44_2_1_2"><span class="lab"><font color="Green" title="E36">A28</font></span></a>, <a class="txt" href="#E12:44_2_1_2"><span class="lab"><font color="Green" title="E38">A30</font></span></a>, <a class="txt" href="#E2:44_2"><span class="lab"><font color="Green" title="E34">A26</font></span></a>, <a class="ref" href="flexary1.html#D4" target="_self" onmouseover="rs('flexary1/D4')" onmouseout="rh()">Def4</a></span>;<br/><a NAME="E14:44_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:44_2_1_2"><span class="lab"><font color="Green" title="E38">A30</font></span></a>, <a class="txt" href="#E1:44"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="pepin.html#T30" onmouseover="rs('pepin/T30')" onmouseout="rh()">PEPIN:30</a></span>;<br/><span class="kw">hence </span><a NAME="E15:44_2_1_2"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c6">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c6">x</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:44_2_1_2"><span class="lab"><font color="Green" title="E38">A30</font></span></a>, <a class="txt" href="#E2:44_2"><span class="lab"><font color="Green" title="E34">A26</font></span></a>, <a class="txt" href="#E3:44_2_1_2"><span class="lab"><font color="Green" title="E36">A28</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a>, <a class="txt" href="#E1:44_2_1_2"><span class="lab"><font color="Green" title="E35">A27</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_2_1_3"><span class="kw">suppose </span></a><a NAME="E1:44_2_1_3"/><span class="lab"><font color="Green" title="E35">A31</font></span>: 
( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c3">f2</font> &amp;  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">f1</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c6">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c6">x</font>)</span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:44_2_1_3"/><span class="lab"><font color="Green" title="E36">A32</font></span>: 
( <font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c3">f2</font> &amp; <font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E4:44_2_1_3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:44_2"><span class="lab"><font color="Green" title="E34">A26</font></span></a>, <a class="txt" href="#E3:44_2_1_3"><span class="lab"><font color="Green" title="E36">A32</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E5:44_2_1_3"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T72" onmouseover="rs('funct_1/T72')" onmouseout="rh()">FUNCT_1:72</a></span>;<br/><a NAME="E6:44_2_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A33</font></span>: 
 <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D17" onmouseover="rs('relat_1/D17')" onmouseout="rh()">RELAT_1:def 17</a></span>;<br/><a NAME="E7:44_2_1_3"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44"><span class="lab"><font color="Green" title="E32">A24</font></span></a>, <a class="ref" href="classes1.html#D10" onmouseover="rs('classes1/D10')" onmouseout="rh()">CLASSES1:def 10</a></span>;<br/><a NAME="E8:44_2_1_3"/><span class="kw">then </span>
 <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:44_2_1_3"><span class="lab"><font color="Green" title="E37">A33</font></span></a></span>;<br/><a NAME="E9:44_2_1_3"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D17" onmouseover="rs('relat_1/D17')" onmouseout="rh()">RELAT_1:def 17</a></span>;<br/><a NAME="E10:44_2_1_3"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T72" onmouseover="rs('funct_1/T72')" onmouseout="rh()">FUNCT_1:72</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E12:44_2_1_3"/><span class="lab"><font color="Green" title="E38">A34</font></span>: 
( <font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E13:44_2_1_3"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">z</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44_2_1_3"><span class="lab"><font color="Green" title="E36">A32</font></span></a>, <a class="txt" href="#E12:44_2_1_3"><span class="lab"><font color="Green" title="E38">A34</font></span></a>, <a class="txt" href="#E2:44_2"><span class="lab"><font color="Green" title="E34">A26</font></span></a>, <a class="ref" href="flexary1.html#D4" target="_self" onmouseover="rs('flexary1/D4')" onmouseout="rh()">Def4</a></span>;<br/><a NAME="E14:44_2_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:44_2_1_3"><span class="lab"><font color="Green" title="E38">A34</font></span></a>, <a class="txt" href="#E1:44"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="pepin.html#T30" onmouseover="rs('pepin/T30')" onmouseout="rh()">PEPIN:30</a></span>;<br/><span class="kw">hence </span><a NAME="E15:44_2_1_3"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c6">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c6">x</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:44_2_1_3"><span class="lab"><font color="Green" title="E38">A34</font></span></a>, <a class="txt" href="#E2:44_2"><span class="lab"><font color="Green" title="E34">A26</font></span></a>, <a class="txt" href="#E3:44_2_1_3"><span class="lab"><font color="Green" title="E36">A32</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a>, <a class="txt" href="#E1:44_2_1_3"><span class="lab"><font color="Green" title="E35">A31</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_2_1_4"><span class="kw">suppose </span></a><a NAME="E1:44_2_1_4"/><span class="lab"><font color="Green" title="E35">A35</font></span>: 
( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c3">f2</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c6">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c6">x</font>)</span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">y1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:44_2_1_4"/><span class="lab"><font color="Green" title="E36">A36</font></span>: 
( <font color="Maroon" title="c7">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E4:44_2_1_4"/><span class="lab"><font color="Green" title="E37">A37</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44_2_1_4"><span class="lab"><font color="Green" title="E36">A36</font></span></a>, <a class="ref" href="flexary1.html#D4" target="_self" onmouseover="rs('flexary1/D4')" onmouseout="rh()">Def4</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c8">y2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E6:44_2_1_4"/><span class="lab"><font color="Green" title="E38">A38</font></span>: 
( <font color="Maroon" title="c8">y2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c3">f2</font> &amp; <font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44_2_1_4"><span class="lab"><font color="Green" title="E35">A35</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><a NAME="E7:44_2_1_4"/><span class="lab"><font color="Green" title="E39">A39</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:44_2_1_4"><span class="lab"><font color="Green" title="E38">A38</font></span></a>, <a class="ref" href="flexary1.html#D4" target="_self" onmouseover="rs('flexary1/D4')" onmouseout="rh()">Def4</a></span>;<br/><a NAME="E8:44_2_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A40</font></span>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y2</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y1</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:44_2_1_4"><span class="lab"><font color="Green" title="E37">A37</font></span></a>, <a class="txt" href="#E6:44_2_1_4"><span class="lab"><font color="Green" title="E38">A38</font></span></a>, <a class="txt" href="#E3:44_2_1_4"><span class="lab"><font color="Green" title="E36">A36</font></span></a>, <a class="txt" href="#E3:44"><span class="lab"><font color="Green" title="E32">A24</font></span></a>, <a class="ref" href="classes1.html#D10" onmouseover="rs('classes1/D10')" onmouseout="rh()">CLASSES1:def 10</a></span>;<br/><a NAME="E9:44_2_1_4"/>
 <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y2</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y2</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="flexary1.html#T28" target="_self" onmouseover="rs('flexary1/T28')" onmouseout="rh()">Th28</a>, <a class="txt" href="#E7:44_2_1_4"><span class="lab"><font color="Green" title="E39">A39</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E10:44_2_1_4"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c6">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f2</font>,<font color="Maroon" title="c6">x</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="flexary1.html#T28" target="_self" onmouseover="rs('flexary1/T28')" onmouseout="rh()">Th28</a>, <a class="txt" href="#E4:44_2_1_4"><span class="lab"><font color="Green" title="E37">A37</font></span></a>, <a class="txt" href="#E8:44_2_1_4"><span class="lab"><font color="Green" title="E40">A40</font></span></a>, <a class="txt" href="#E3:44_2_1_4"><span class="lab"><font color="Green" title="E36">A36</font></span></a>, <a class="txt" href="#E6:44_2_1_4"><span class="lab"><font color="Green" title="E38">A38</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:44"/>
<font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">f2</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="classes1.html#D10" onmouseover="rs('classes1/D10')" onmouseout="rh()">CLASSES1:def 10</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
