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

<span class="kw">let </span><font color="Maroon" title="c1">f1</font>, <font color="Maroon" title="c2">f2</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="funct_6.html#K7" title="FUNCT_6:func.7">Frege</a> <span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f1</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="funct_6.html#K7" title="FUNCT_6:func.7">Frege</a> <span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f1</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">f2</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> &amp; (  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f1</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">f2</font> holds <br/><span class="p1">(<span class="default"><a href="funct_6.html#K7" title="FUNCT_6:func.7">Frege</a> <span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">y</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> ) )</span><br/>



<a NAME="E1:151"/><span class="lab"><font color="Green" title="E86">A1</font></span>: 
 <a href="funct_6.html#K3" title="FUNCT_6:func.3">rngs</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f1</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">f2</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T133" target="_self" title="FINSEQ_3:th.133">Th34</a></span>;<br/>
<a NAME="E2:151"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f1</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">f2</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/>
<a NAME="E3:151"/><span class="kw">then </span><span class="lab"><font color="Green" title="E87">A2</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f1</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">f2</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E4:151"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/>
<a NAME="E5:151"/><span class="kw">then </span><span class="lab"><font color="Green" title="E88">A3</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E6:151"/><span class="lab"><font color="Green" title="E89">A4</font></span>: 
 <a href="funct_6.html#K2" title="FUNCT_6:func.2">doms</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f1</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T133" target="_self" title="FINSEQ_3:th.133">Th34</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:151"/>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="funct_6.html#K7" title="FUNCT_6:func.7">Frege</a> <span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f1</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="funct_6.html#K7" title="FUNCT_6:func.7">Frege</a> <span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f1</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">f2</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:151"><span class="lab"><font color="Green" title="E86">A1</font></span></a>, <a class="ref" href="funct_6.html#T38" title="FUNCT_6:th.38">FUNCT_6:38</a>, <a class="ref" href="funct_6.html#D7" title="FUNCT_6:def.7">FUNCT_6:def 7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f1</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">f2</font> holds <br/><span class="p1">(<span class="default"><a href="funct_6.html#K7" title="FUNCT_6:func.7">Frege</a> <span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">y</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f1</font> &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">f2</font> implies <span class="p1">(<span class="default"><a href="funct_6.html#K7" title="FUNCT_6:func.7">Frege</a> <span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">y</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> )</span><br/>



<span class="kw">assume </span><a NAME="E8:151"/>
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f1</font> &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">f2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="funct_6.html#K7" title="FUNCT_6:func.7">Frege</a> <span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">y</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><br/>

<a NAME="E9:151"/><span class="kw">then </span><span class="lab"><font color="Green" title="E90">A5</font></span>: 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="funct_6.html#K2" title="FUNCT_6:func.2">doms</a> <span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:151"><span class="lab"><font color="Green" title="E89">A4</font></span></a>, <a class="ref" href="finseq_3.html#T124" target="_self" title="FINSEQ_3:th.124">Th2</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><br/><a NAME="E11:151"/><span class="lab"><font color="Green" title="E91">A6</font></span>: 
<span class="p1">(<span class="default"><a href="funct_6.html#K7" title="FUNCT_6:func.7">Frege</a> <span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font>
 <span class="kw">and </span><br/><a NAME="E12:151"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <span class="p1">(<span class="default"><a href="funct_6.html#K1" title="FUNCT_6:func.1">SubFuncs</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E13:151"/>
 for <font color="Olive" title="b1">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">f</font> holds <br/><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="funct_5.html#K2" title="FUNCT_5:func.2">uncurry</a> <span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">z</font>,<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">z</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_6.html#D7" title="FUNCT_6:def.7">FUNCT_6:def 7</a></span>;<br/>
<a NAME="E14:151"/><span class="lab"><font color="Green" title="E92">A7</font></span>: 
( <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> &amp; <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/>
<a NAME="E15:151"/><span class="lab"><font color="Green" title="E93">A8</font></span>: 
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2 &amp; <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">f1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T2" title="FINSEQ_1:th.2">FINSEQ_1:2</a>, <a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<a NAME="E16:151"/><span class="kw">then </span>
<font color="Maroon" title="c5">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="funct_6.html#K3" title="FUNCT_6:func.3">rngs</a> <span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:151"><span class="lab"><font color="Green" title="E88">A3</font></span></a>, <a class="txt" href="#E9:151"><span class="lab"><font color="Green" title="E90">A5</font></span></a>, <a class="txt" href="#E11:151"><span class="lab"><font color="Green" title="E91">A6</font></span></a>, <a class="ref" href="funct_6.html#T37" title="FUNCT_6:th.37">FUNCT_6:37</a></span>;<br/>
<a NAME="E17:151"/><span class="kw">then </span><span class="lab"><font color="Green" title="E94">A9</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:151"><span class="lab"><font color="Green" title="E86">A1</font></span></a>, <a class="txt" href="#E3:151"><span class="lab"><font color="Green" title="E87">A2</font></span></a>, <a class="ref" href="card_3.html#T9" title="CARD_3:th.9">CARD_3:9</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">f</font> = <font color="Maroon" title="c5">f</font> as   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D2" title="FINSEQ_1:def.2">FINSEQ_1:def 2</a></span>;<br/>
<a NAME="E19:151"/>
( 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2 &amp; <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T2" title="FINSEQ_1:th.2">FINSEQ_1:2</a>, <a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<a NAME="E20:151"/><span class="kw">then </span><span class="lab"><font color="Green" title="E95">A10</font></span>: 
<font color="Maroon" title="c6">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:151"><span class="lab"><font color="Green" title="E88">A3</font></span></a>, <a class="txt" href="#E9:151"><span class="lab"><font color="Green" title="E90">A5</font></span></a>, <a class="txt" href="#E11:151"><span class="lab"><font color="Green" title="E91">A6</font></span></a>, <a class="ref" href="funct_6.html#T37" title="FUNCT_6:th.37">FUNCT_6:37</a></span>;<br/>
<a NAME="E21:151"/><span class="lab"><font color="Green" title="E96">A11</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:151"><span class="lab"><font color="Green" title="E94">A9</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E22:151"/>
<font color="Maroon" title="c6">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:151"><span class="lab"><font color="Green" title="E88">A3</font></span></a>, <a class="txt" href="#E15:151"><span class="lab"><font color="Green" title="E93">A8</font></span></a>, <a class="txt" href="#E9:151"><span class="lab"><font color="Green" title="E90">A5</font></span></a>, <a class="txt" href="#E11:151"><span class="lab"><font color="Green" title="E91">A6</font></span></a>, <a class="ref" href="funct_6.html#T37" title="FUNCT_6:th.37">FUNCT_6:37</a></span>;<br/>
<span class="kw">hence </span><a NAME="E23:151"/>
<span class="p1">(<span class="default"><a href="funct_6.html#K7" title="FUNCT_6:func.7">Frege</a> <span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">y</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:151"><span class="lab"><font color="Green" title="E91">A6</font></span></a>, <a class="txt" href="#E20:151"><span class="lab"><font color="Green" title="E95">A10</font></span></a>, <a class="txt" href="#E21:151"><span class="lab"><font color="Green" title="E96">A11</font></span></a>, <a class="txt" href="#E14:151"><span class="lab"><font color="Green" title="E92">A7</font></span></a>, <a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
