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

<span class="kw">consider </span><font color="Maroon" title="c4">h2</font>, <font color="Maroon" title="c5">h1</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span><span class="kw"> such that </span><br/><a NAME="E2:19_1_1"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
(  not <font color="Maroon" title="c4">h2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp;  not <font color="Maroon" title="c5">h1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp;  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c5">h1</font> )
 <span class="kw">and </span><br/><a NAME="E3:19_1_1"/><span class="lab"><font color="Green" title="E19">A3</font></span>: 
 <a href="cat_6.html#K5" title="CAT_6:func.5">Ob</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 <span class="kw">and </span><br/><a NAME="E4:19_1_1"/><span class="lab"><font color="Green" title="E20">A4</font></span>: 
 <a href="cat_6.html#K1" title="CAT_6:func.1">Mor</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2">(<span class="default"><a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font></span>)</span>,<font color="Maroon" title="c4">h2</font>,<font color="Maroon" title="c5">h1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font></span>)</span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <span class="kw">and </span><br/><a NAME="E5:19_1_1"/><span class="lab"><font color="Green" title="E21">A5</font></span>: 
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font>, <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font>, <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>,<font color="Maroon" title="c4">h2</font>,<font color="Maroon" title="c5">h1</font>,<font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> <a href="zfmisc_1.html#R4" title="ZFMISC_1:pred.4">are_mutually_distinct</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_8.html#T18" target="_self" onmouseover="rs('cat_8/T18')" onmouseout="rh()">Th18</a></span>;<br/>
<a NAME="E6:19_1_1"/><span class="lab"><font color="Green" title="E22">A6</font></span>: 
<font color="Maroon" title="c5">h1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c4">h2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19_1_1"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/>
<a NAME="E7:19_1_1"/><span class="lab"><font color="Green" title="E23">A7</font></span>: 
 ex <font color="Olive" title="b1">F</font> being   <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>,<font color="Maroon" title="c1">C</font> st <br/> for <font color="Olive" title="b2">g1</font>, <font color="Olive" title="b3">g2</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b2">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Olive" title="b3">g2</font> &amp;  not <font color="Olive" title="b2">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp;  not <font color="Olive" title="b3">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  holds <br/>( <font color="Olive" title="b1">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b2">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Olive" title="b1">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b3">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="19_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ] <span class="kw">means </span>( ( $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c3">f2</font> ) &amp; ( $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c3">f2</font> ) &amp; ( $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c2">f1</font> ) &amp; ( $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> ) &amp; ( $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> ) &amp; ( $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c3">f2</font> ) );<br/>
<a NAME="E1:19_1_1_1"/><span class="lab"><font color="Green" title="E24">A8</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span> holds <br/> ex <font color="Olive" title="b2">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>] )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="19_1_1_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"> ( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span> implies  ex <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Olive" title="b1">y</font>] ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:19_1_1_1_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</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">  ex <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Olive" title="b1">y</font>] )</span><br/>

<a NAME="E2:19_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A9</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2">(<span class="default"><a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font></span>)</span>,<font color="Maroon" title="c4">h2</font>,<font color="Maroon" title="c5">h1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font></span>)</span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D1" onmouseover="rs('cat_6/D1')" onmouseout="rh()">CAT_6:def 1</a>, <a class="txt" href="#E4:19_1_1"><span class="lab"><font color="Green" title="E20">A4</font></span></a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_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="E1:19_1_1_1_1_1"/>
( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19_1_1_1_1"><span class="lab"><font color="Green" title="E25">A9</font></span></a>, <a class="ref" href="enumset1.html#D4" onmouseover="rs('enumset1/D4')" onmouseout="rh()">ENUMSET1:def 4</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_1_1_1"/><span class="lab"><font color="Green" title="E26">A10</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</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">  ex <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Olive" title="b1">y</font>] )</span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c7">y</font> =  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c3">f2</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  ;<br/><span class="kw">take </span>
<font color="Maroon" title="c7">y</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"> ( <font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>] )</span><br/><a NAME="E3:19_1_1_1_1_1_1"/>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_6.html#K5" title="CAT_6:func.5">Ob</a> <font color="Maroon" title="c1">C</font>
 ;<br/><a NAME="E4:19_1_1_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_6.html#K1" title="CAT_6:func.1">Mor</a> <font color="Maroon" title="c1">C</font>
 ;<br/><span class="kw">hence </span><a NAME="E5:19_1_1_1_1_1_1"/>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D1" onmouseover="rs('cat_6/D1')" onmouseout="rh()">CAT_6:def 1</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"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>]</span><br/><span class="kw">thus </span><a NAME="E6:19_1_1_1_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_1_1_1"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E26">A11</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</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">  ex <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Olive" title="b1">y</font>] )</span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c7">y</font> =  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c3">f2</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  ;<br/><span class="kw">take </span>
<font color="Maroon" title="c7">y</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"> ( <font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>] )</span><br/><a NAME="E3:19_1_1_1_1_1_2"/>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_6.html#K5" title="CAT_6:func.5">Ob</a> <font color="Maroon" title="c1">C</font>
 ;<br/><a NAME="E4:19_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_6.html#K1" title="CAT_6:func.1">Mor</a> <font color="Maroon" title="c1">C</font>
 ;<br/><span class="kw">hence </span><a NAME="E5:19_1_1_1_1_1_2"/>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D1" onmouseover="rs('cat_6/D1')" onmouseout="rh()">CAT_6:def 1</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"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>]</span><br/><span class="kw">thus </span><a NAME="E6:19_1_1_1_1_1_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E26">A11</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_1_1_3"/><span class="lab"><font color="Green" title="E26">A12</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</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">  ex <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Olive" title="b1">y</font>] )</span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c7">y</font> =  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c2">f1</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  ;<br/><span class="kw">take </span>
<font color="Maroon" title="c7">y</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"> ( <font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>] )</span><br/><a NAME="E3:19_1_1_1_1_1_3"/>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_6.html#K5" title="CAT_6:func.5">Ob</a> <font color="Maroon" title="c1">C</font>
 ;<br/><a NAME="E4:19_1_1_1_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_6.html#K1" title="CAT_6:func.1">Mor</a> <font color="Maroon" title="c1">C</font>
 ;<br/><span class="kw">hence </span><a NAME="E5:19_1_1_1_1_1_3"/>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D1" onmouseover="rs('cat_6/D1')" onmouseout="rh()">CAT_6:def 1</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"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>]</span><br/><span class="kw">thus </span><a NAME="E6:19_1_1_1_1_1_3"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_1_1_3"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_1_1_4"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_1_1_4"/><span class="lab"><font color="Green" title="E26">A13</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</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">  ex <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Olive" title="b1">y</font>] )</span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c7">y</font> = <font color="Maroon" title="c3">f2</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  ;<br/><span class="kw">take </span>
<font color="Maroon" title="c7">y</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"> ( <font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>] )</span><br/><a NAME="E3:19_1_1_1_1_1_4"/>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_6.html#K1" title="CAT_6:func.1">Mor</a> <font color="Maroon" title="c1">C</font>
 ;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_1_1_4"/>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D1" onmouseover="rs('cat_6/D1')" onmouseout="rh()">CAT_6:def 1</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"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>]</span><br/><span class="kw">thus </span><a NAME="E5:19_1_1_1_1_1_4"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_1_1_4"><span class="lab"><font color="Green" title="E26">A13</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_1_1_5"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_1_1_5"/><span class="lab"><font color="Green" title="E26">A14</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</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">  ex <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Olive" title="b1">y</font>] )</span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c7">y</font> = <font color="Maroon" title="c2">f1</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  ;<br/><span class="kw">take </span>
<font color="Maroon" title="c7">y</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"> ( <font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>] )</span><br/><a NAME="E3:19_1_1_1_1_1_5"/>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_6.html#K1" title="CAT_6:func.1">Mor</a> <font color="Maroon" title="c1">C</font>
 ;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_1_1_5"/>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D1" onmouseover="rs('cat_6/D1')" onmouseout="rh()">CAT_6:def 1</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"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>]</span><br/><span class="kw">thus </span><a NAME="E5:19_1_1_1_1_1_5"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_1_1_5"><span class="lab"><font color="Green" title="E26">A14</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_1_1_6"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_1_1_6"/><span class="lab"><font color="Green" title="E26">A15</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</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">  ex <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Olive" title="b1">y</font>] )</span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c7">y</font> = <font color="Maroon" title="c2">f1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c3">f2</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  ;<br/><span class="kw">take </span>
<font color="Maroon" title="c7">y</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"> ( <font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>] )</span><br/><a NAME="E3:19_1_1_1_1_1_6"/>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_6.html#K1" title="CAT_6:func.1">Mor</a> <font color="Maroon" title="c1">C</font>
 ;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_1_1_6"/>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D1" onmouseover="rs('cat_6/D1')" onmouseout="rh()">CAT_6:def 1</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"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>]</span><br/><span class="kw">thus </span><a NAME="E5:19_1_1_1_1_1_6"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_1_1_6"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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">consider </span><font color="Maroon" title="c6">F</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font><span class="kw"> such that </span><br/><a NAME="E3:19_1_1_1"/><span class="lab"><font color="Green" title="E25">A16</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>]
 <span class="kw">from</span> <span class="lab"><a class="ref" href="funct_2.html#S1" onmouseover="rs('funct_2/S1')" onmouseout="rh()">FUNCT_2:sch 1</a>(<a class="txt" href="#E1:19_1_1_1"><span class="lab"><font color="Green" title="E24">A8</font></span></a>);<br/></span>
<span class="kw">reconsider </span><font color="Maroon" title="c7">F</font> = <font color="Maroon" title="c6">F</font> as   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>,<font color="Maroon" title="c1">C</font> ;<br/>
<a NAME="E5:19_1_1_1"/>
 for <font color="Olive" title="b1">g</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b1">g</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  holds <br/><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b1">g</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a> 
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">g</font> be   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</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"> ( <font color="Maroon" title="c8">g</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  implies <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:19_1_1_1_2"/><span class="lab"><font color="Green" title="E26">A17</font></span>: 
<font color="Maroon" title="c8">g</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</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="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a> </span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c9">x</font> = <font color="Maroon" title="c8">g</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  ;<br/>
<a NAME="E3:19_1_1_1_2"/><span class="lab"><font color="Green" title="E27">A18</font></span>: 
<font color="Maroon" title="c7">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D21" onmouseover="rs('cat_6/D21')" onmouseout="rh()">CAT_6:def 21</a></span>;<br/>
<a NAME="E4:19_1_1_1_2"/>
<font color="Maroon" title="c8">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cat_6.html#K1" title="CAT_6:func.1">Mor</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>
 
;<br/>
<a NAME="E5:19_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D1" onmouseover="rs('cat_6/D1')" onmouseout="rh()">CAT_6:def 1</a></span>;<br/>
<a NAME="E6:19_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A19</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c9">x</font>,<font color="Maroon" title="c7">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font>]
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:19_1_1_1"><span class="lab"><font color="Green" title="E25">A16</font></span></a></span>;<br/>
<a NAME="E7:19_1_1_1_2"/>
<font color="Maroon" title="c8">g</font> is   <a href="cat_6.html#NM3" title="CAT_6:NM.3">Object</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_2"><span class="lab"><font color="Green" title="E26">A17</font></span></a>, <a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:19_1_1_1_2"/>
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1_1_2"><span class="lab"><font color="Green" title="E28">A19</font></span></a>, <a class="txt" href="#E3:19_1_1_1_2"><span class="lab"><font color="Green" title="E27">A18</font></span></a>, <a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a>, <a class="txt" href="#E3:19_1_1"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</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>
<a NAME="E6:19_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A20</font></span>: 
<font color="Maroon" title="c7">F</font> is  <a href="cat_6.html#V13" title="CAT_6:attr.13">identity-preserving</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D22" onmouseover="rs('cat_6/D22')" onmouseout="rh()">CAT_6:def 22</a></span>;<br/>
<a NAME="E7:19_1_1_1"/><span class="lab"><font color="Green" title="E27">A21</font></span>: 
 for <font color="Olive" title="b1">g</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> holds <br/><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">g</font> be   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</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"> ( <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> implies <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:19_1_1_1_3"/><span class="lab"><font color="Green" title="E28">A22</font></span>: 
<font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</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"> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c9">x</font> = <font color="Maroon" title="c8">g</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  ;<br/>
<a NAME="E3:19_1_1_1_3"/><span class="lab"><font color="Green" title="E29">A23</font></span>: 
<font color="Maroon" title="c7">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D21" onmouseover="rs('cat_6/D21')" onmouseout="rh()">CAT_6:def 21</a></span>;<br/>
<a NAME="E4:19_1_1_1_3"/>
<font color="Maroon" title="c8">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cat_6.html#K1" title="CAT_6:func.1">Mor</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>
 
;<br/>
<a NAME="E5:19_1_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D1" onmouseover="rs('cat_6/D1')" onmouseout="rh()">CAT_6:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:19_1_1_1_3"/>
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:19_1_1_1"><span class="lab"><font color="Green" title="E25">A16</font></span></a>, <a class="txt" href="#E1:19_1_1_1_3"><span class="lab"><font color="Green" title="E28">A22</font></span></a>, <a class="txt" href="#E3:19_1_1_1_3"><span class="lab"><font color="Green" title="E29">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>
<a NAME="E8:19_1_1_1"/><span class="lab"><font color="Green" title="E28">A24</font></span>: 
 for <font color="Olive" title="b1">g</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> holds <br/><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">g</font> be   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</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"> ( <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> implies <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:19_1_1_1_4"/><span class="lab"><font color="Green" title="E29">A25</font></span>: 
<font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</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"> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c9">x</font> = <font color="Maroon" title="c8">g</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  ;<br/>
<a NAME="E3:19_1_1_1_4"/><span class="lab"><font color="Green" title="E30">A26</font></span>: 
<font color="Maroon" title="c7">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D21" onmouseover="rs('cat_6/D21')" onmouseout="rh()">CAT_6:def 21</a></span>;<br/>
<a NAME="E4:19_1_1_1_4"/>
<font color="Maroon" title="c8">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cat_6.html#K1" title="CAT_6:func.1">Mor</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>
 
;<br/>
<a NAME="E5:19_1_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D1" onmouseover="rs('cat_6/D1')" onmouseout="rh()">CAT_6:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:19_1_1_1_4"/>
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:19_1_1_1"><span class="lab"><font color="Green" title="E25">A16</font></span></a>, <a class="txt" href="#E1:19_1_1_1_4"><span class="lab"><font color="Green" title="E29">A25</font></span></a>, <a class="txt" href="#E3:19_1_1_1_4"><span class="lab"><font color="Green" title="E30">A26</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>
<a NAME="E9:19_1_1_1"/>
 for <font color="Olive" title="b1">g1</font>, <font color="Olive" title="b2">g2</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b1">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Olive" title="b2">g2</font> holds <br/>( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b1">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b2">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Olive" title="b2">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b1">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b2">g2</font></span>)</span> )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">g1</font>, <font color="Maroon" title="c9">g2</font> be   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</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"> ( <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c9">g2</font> implies ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:19_1_1_1_5"/><span class="lab"><font color="Green" title="E29">A27</font></span>: 
<font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c9">g2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/>

<a NAME="E2:19_1_1_1_5"/><span class="lab"><font color="Green" title="E30">A28</font></span>: 
 for <font color="Olive" title="b1">g</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> holds <br/><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c3">f2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_5_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c10">g</font> be   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</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"> ( <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> implies <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c3">f2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:19_1_1_1_5_1"/><span class="lab"><font color="Green" title="E31">A29</font></span>: 
<font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</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"> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c3">f2</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c11">x</font> = <font color="Maroon" title="c10">g</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  ;<br/>
<a NAME="E3:19_1_1_1_5_1"/><span class="lab"><font color="Green" title="E32">A30</font></span>: 
<font color="Maroon" title="c7">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D21" onmouseover="rs('cat_6/D21')" onmouseout="rh()">CAT_6:def 21</a></span>;<br/>
<a NAME="E4:19_1_1_1_5_1"/>
<font color="Maroon" title="c10">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cat_6.html#K1" title="CAT_6:func.1">Mor</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>
 
;<br/>
<a NAME="E5:19_1_1_1_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D1" onmouseover="rs('cat_6/D1')" onmouseout="rh()">CAT_6:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:19_1_1_1_5_1"/>
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c3">f2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:19_1_1_1"><span class="lab"><font color="Green" title="E25">A16</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5_1"><span class="lab"><font color="Green" title="E31">A29</font></span></a>, <a class="txt" href="#E3:19_1_1_1_5_1"><span class="lab"><font color="Green" title="E32">A30</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>
<a NAME="E3:19_1_1_1_5"/><span class="lab"><font color="Green" title="E31">A31</font></span>: 
 for <font color="Olive" title="b1">g</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> holds <br/><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c3">f2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_5_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c10">g</font> be   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</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"> ( <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> implies <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c3">f2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:19_1_1_1_5_2"/><span class="lab"><font color="Green" title="E32">A32</font></span>: 
<font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</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"> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c3">f2</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c11">x</font> = <font color="Maroon" title="c10">g</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  ;<br/>
<a NAME="E3:19_1_1_1_5_2"/><span class="lab"><font color="Green" title="E33">A33</font></span>: 
<font color="Maroon" title="c7">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D21" onmouseover="rs('cat_6/D21')" onmouseout="rh()">CAT_6:def 21</a></span>;<br/>
<a NAME="E4:19_1_1_1_5_2"/>
<font color="Maroon" title="c10">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cat_6.html#K1" title="CAT_6:func.1">Mor</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>
 
;<br/>
<a NAME="E5:19_1_1_1_5_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D1" onmouseover="rs('cat_6/D1')" onmouseout="rh()">CAT_6:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:19_1_1_1_5_2"/>
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c3">f2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:19_1_1_1"><span class="lab"><font color="Green" title="E25">A16</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5_2"><span class="lab"><font color="Green" title="E32">A32</font></span></a>, <a class="txt" href="#E3:19_1_1_1_5_2"><span class="lab"><font color="Green" title="E33">A33</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>
<a NAME="E4:19_1_1_1_5"/><span class="lab"><font color="Green" title="E32">A34</font></span>: 
 for <font color="Olive" title="b1">g</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> holds <br/><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c2">f1</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_5_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c10">g</font> be   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</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"> ( <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> implies <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c2">f1</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:19_1_1_1_5_3"/><span class="lab"><font color="Green" title="E33">A35</font></span>: 
<font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</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"> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c2">f1</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c11">x</font> = <font color="Maroon" title="c10">g</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  ;<br/>
<a NAME="E3:19_1_1_1_5_3"/><span class="lab"><font color="Green" title="E34">A36</font></span>: 
<font color="Maroon" title="c7">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D21" onmouseover="rs('cat_6/D21')" onmouseout="rh()">CAT_6:def 21</a></span>;<br/>
<a NAME="E4:19_1_1_1_5_3"/>
<font color="Maroon" title="c10">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cat_6.html#K1" title="CAT_6:func.1">Mor</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>
 
;<br/>
<a NAME="E5:19_1_1_1_5_3"/><span class="kw">then </span>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D1" onmouseover="rs('cat_6/D1')" onmouseout="rh()">CAT_6:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:19_1_1_1_5_3"/>
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c2">f1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:19_1_1_1"><span class="lab"><font color="Green" title="E25">A16</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5_3"><span class="lab"><font color="Green" title="E33">A35</font></span></a>, <a class="txt" href="#E3:19_1_1_1_5_3"><span class="lab"><font color="Green" title="E34">A36</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>
<a NAME="E5:19_1_1_1_5"/><span class="lab"><font color="Green" title="E33">A37</font></span>: 
 for <font color="Olive" title="b1">g</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> holds <br/><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c3">f2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_5_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c10">g</font> be   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</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"> ( <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> implies <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c3">f2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:19_1_1_1_5_4"/><span class="lab"><font color="Green" title="E34">A38</font></span>: 
<font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</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"> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c3">f2</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c11">x</font> = <font color="Maroon" title="c10">g</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  ;<br/>
<a NAME="E3:19_1_1_1_5_4"/><span class="lab"><font color="Green" title="E35">A39</font></span>: 
<font color="Maroon" title="c7">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D21" onmouseover="rs('cat_6/D21')" onmouseout="rh()">CAT_6:def 21</a></span>;<br/>
<a NAME="E4:19_1_1_1_5_4"/>
<font color="Maroon" title="c10">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cat_6.html#K1" title="CAT_6:func.1">Mor</a> <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>
 
;<br/>
<a NAME="E5:19_1_1_1_5_4"/><span class="kw">then </span>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D1" onmouseover="rs('cat_6/D1')" onmouseout="rh()">CAT_6:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:19_1_1_1_5_4"/>
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c3">f2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:19_1_1_1"><span class="lab"><font color="Green" title="E25">A16</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5_4"><span class="lab"><font color="Green" title="E34">A38</font></span></a>, <a class="txt" href="#E3:19_1_1_1_5_4"><span class="lab"><font color="Green" title="E35">A39</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="19_1_1_1_5_5"><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="E1:19_1_1_1_5_5"/>
( ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> ) or ( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:19_1_1"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="ref" href="enumset1.html#D4" onmouseover="rs('enumset1/D4')" onmouseout="rh()">ENUMSET1:def 4</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_5_5_1"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_1"/><span class="lab"><font color="Green" title="E34">A40</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A41</font></span>: 
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c3">f2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c3">f2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19_1_1_1_5"><span class="lab"><font color="Green" title="E30">A28</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_5_5_1"/><span class="lab"><font color="Green" title="E36">A42</font></span>: 
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#T23" onmouseover="rs('cat_6/T23')" onmouseout="rh()">CAT_6:23</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"> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span></span><br/><span class="kw">thus </span><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> = 
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_1"><span class="lab"><font color="Green" title="E34">A40</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_6.html#T23" onmouseover="rs('cat_6/T23')" onmouseout="rh()">CAT_6:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:19_1_1_1_5_5_1"><span class="lab"><font color="Green" title="E36">A42</font></span></a>, <a class="txt" href="#E2:19_1_1_1_5_5_1"><span class="lab"><font color="Green" title="E35">A41</font></span></a>, <a class="ref" href="cat_6.html#T23" onmouseover="rs('cat_6/T23')" onmouseout="rh()">CAT_6:23</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="19_1_1_1_5_5_2"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_2"/><span class="lab"><font color="Green" title="E34">A43</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_2"/><span class="kw">then </span>
( <font color="Maroon" title="c8">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp; <font color="Maroon" title="c9">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a></span>;<br/><a NAME="E3:19_1_1_1_5_5_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_7.html#T7" onmouseover="rs('cat_7/T7')" onmouseout="rh()">CAT_7:7</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_5_5_2"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_2"><span class="lab"><font color="Green" title="E34">A43</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_3"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_3"/><span class="lab"><font color="Green" title="E34">A44</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_3"/><span class="kw">then </span>
( <font color="Maroon" title="c8">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp; <font color="Maroon" title="c9">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a></span>;<br/><a NAME="E3:19_1_1_1_5_5_3"/><span class="kw">then </span>
<font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_7.html#T7" onmouseover="rs('cat_7/T7')" onmouseout="rh()">CAT_7:7</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_5_5_3"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_3"><span class="lab"><font color="Green" title="E34">A44</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_4"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_4"/><span class="lab"><font color="Green" title="E34">A45</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_4"/><span class="kw">then </span>
 <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a>, <a class="ref" href="cat_6.html#T27" onmouseover="rs('cat_6/T27')" onmouseout="rh()">CAT_6:27</a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_5_5_4"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_4"><span class="lab"><font color="Green" title="E34">A45</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_5"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_5"/><span class="lab"><font color="Green" title="E34">A46</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_5"/><span class="kw">then </span>
 <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a>, <a class="ref" href="cat_6.html#T27" onmouseover="rs('cat_6/T27')" onmouseout="rh()">CAT_6:27</a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_5_5_5"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_5"><span class="lab"><font color="Green" title="E34">A46</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_6"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_6"/><span class="lab"><font color="Green" title="E34">A47</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_6"/><span class="kw">then </span>
 <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a>, <a class="ref" href="cat_6.html#T27" onmouseover="rs('cat_6/T27')" onmouseout="rh()">CAT_6:27</a></span>;<br/><a NAME="E3:19_1_1_1_5_5_6"/><span class="kw">then </span>
 <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_5_5_6"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_6"><span class="lab"><font color="Green" title="E34">A47</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_7"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_7"/><span class="lab"><font color="Green" title="E34">A48</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_7"/><span class="kw">then </span>
( <font color="Maroon" title="c8">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp; <font color="Maroon" title="c9">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a></span>;<br/><a NAME="E3:19_1_1_1_5_5_7"/><span class="kw">then </span>
<font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_7.html#T7" onmouseover="rs('cat_7/T7')" onmouseout="rh()">CAT_7:7</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_5_5_7"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_7"><span class="lab"><font color="Green" title="E34">A48</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_8"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_8"/><span class="lab"><font color="Green" title="E34">A49</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A50</font></span>: 
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c3">f2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c3">f2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:19_1_1_1_5"><span class="lab"><font color="Green" title="E31">A31</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_5_5_8"/><span class="lab"><font color="Green" title="E36">A51</font></span>: 
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#T23" onmouseover="rs('cat_6/T23')" onmouseout="rh()">CAT_6:23</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"> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span></span><br/><span class="kw">thus </span><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> = 
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_8"><span class="lab"><font color="Green" title="E34">A49</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_6.html#T23" onmouseover="rs('cat_6/T23')" onmouseout="rh()">CAT_6:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:19_1_1_1_5_5_8"><span class="lab"><font color="Green" title="E36">A51</font></span></a>, <a class="txt" href="#E2:19_1_1_1_5_5_8"><span class="lab"><font color="Green" title="E35">A50</font></span></a>, <a class="ref" href="cat_6.html#T23" onmouseover="rs('cat_6/T23')" onmouseout="rh()">CAT_6:23</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="19_1_1_1_5_5_9"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_9"/><span class="lab"><font color="Green" title="E34">A52</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_9"/><span class="kw">then </span>
( <font color="Maroon" title="c8">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp; <font color="Maroon" title="c9">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a></span>;<br/><a NAME="E3:19_1_1_1_5_5_9"/><span class="kw">then </span>
<font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_7.html#T7" onmouseover="rs('cat_7/T7')" onmouseout="rh()">CAT_7:7</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_5_5_9"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_9"><span class="lab"><font color="Green" title="E34">A52</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_10"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_10"/><span class="lab"><font color="Green" title="E34">A53</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A54</font></span>: 
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c3">f2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:19_1_1_1_5"><span class="lab"><font color="Green" title="E31">A31</font></span></a>, <a class="txt" href="#E7:19_1_1_1"><span class="lab"><font color="Green" title="E27">A21</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_5_5_10"/>
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_7.html#T9" onmouseover="rs('cat_7/T9')" onmouseout="rh()">CAT_7:9</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"> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span></span><br/><span class="kw">thus </span><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> = 
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_10"><span class="lab"><font color="Green" title="E34">A53</font></span></a>, <a class="ref" href="cat_7.html#T9" onmouseover="rs('cat_7/T9')" onmouseout="rh()">CAT_7:9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19_1_1_1_5_5_10"><span class="lab"><font color="Green" title="E35">A54</font></span></a>, <a class="ref" href="cat_7.html#T9" onmouseover="rs('cat_7/T9')" onmouseout="rh()">CAT_7:9</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="19_1_1_1_5_5_11"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_11"/><span class="lab"><font color="Green" title="E34">A55</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_11"/><span class="kw">then </span>
 <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a>, <a class="ref" href="cat_6.html#T27" onmouseover="rs('cat_6/T27')" onmouseout="rh()">CAT_6:27</a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_5_5_11"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_11"><span class="lab"><font color="Green" title="E34">A55</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_12"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_12"/><span class="lab"><font color="Green" title="E34">A56</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_12"/><span class="kw">then </span>
 <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a>, <a class="ref" href="cat_6.html#T27" onmouseover="rs('cat_6/T27')" onmouseout="rh()">CAT_6:27</a></span>;<br/><a NAME="E3:19_1_1_1_5_5_12"/><span class="kw">then </span>
 <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_5_5_12"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_12"><span class="lab"><font color="Green" title="E34">A56</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_13"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_13"/><span class="lab"><font color="Green" title="E34">A57</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_13"/><span class="kw">then </span>
( <font color="Maroon" title="c8">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp; <font color="Maroon" title="c9">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a></span>;<br/><a NAME="E3:19_1_1_1_5_5_13"/><span class="kw">then </span>
<font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_7.html#T7" onmouseover="rs('cat_7/T7')" onmouseout="rh()">CAT_7:7</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_5_5_13"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_13"><span class="lab"><font color="Green" title="E34">A57</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_14"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_14"/><span class="lab"><font color="Green" title="E34">A58</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_14"/><span class="kw">then </span>
( <font color="Maroon" title="c8">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp; <font color="Maroon" title="c9">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a></span>;<br/><a NAME="E3:19_1_1_1_5_5_14"/><span class="kw">then </span>
<font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_7.html#T7" onmouseover="rs('cat_7/T7')" onmouseout="rh()">CAT_7:7</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_5_5_14"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_14"><span class="lab"><font color="Green" title="E34">A58</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_15"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_15"/><span class="lab"><font color="Green" title="E34">A59</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_15"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A60</font></span>: 
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c2">f1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:19_1_1_1_5"><span class="lab"><font color="Green" title="E32">A34</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_5_5_15"/><span class="lab"><font color="Green" title="E36">A61</font></span>: 
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#T23" onmouseover="rs('cat_6/T23')" onmouseout="rh()">CAT_6:23</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"> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span></span><br/><span class="kw">thus </span><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> = 
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_15"><span class="lab"><font color="Green" title="E34">A59</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_6.html#T23" onmouseover="rs('cat_6/T23')" onmouseout="rh()">CAT_6:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:19_1_1_1_5_5_15"><span class="lab"><font color="Green" title="E36">A61</font></span></a>, <a class="txt" href="#E2:19_1_1_1_5_5_15"><span class="lab"><font color="Green" title="E35">A60</font></span></a>, <a class="ref" href="cat_6.html#T23" onmouseover="rs('cat_6/T23')" onmouseout="rh()">CAT_6:23</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="19_1_1_1_5_5_16"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_16"/><span class="lab"><font color="Green" title="E34">A62</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_16"/><span class="kw">then </span>
 <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a>, <a class="ref" href="cat_6.html#T27" onmouseover="rs('cat_6/T27')" onmouseout="rh()">CAT_6:27</a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_5_5_16"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_16"><span class="lab"><font color="Green" title="E34">A62</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_17"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_17"/><span class="lab"><font color="Green" title="E34">A63</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A64</font></span>: 
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:19_1_1_1_5"><span class="lab"><font color="Green" title="E32">A34</font></span></a>, <a class="txt" href="#E8:19_1_1_1"><span class="lab"><font color="Green" title="E28">A24</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_5_5_17"/>
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_7.html#T9" onmouseover="rs('cat_7/T9')" onmouseout="rh()">CAT_7:9</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"> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span></span><br/><span class="kw">thus </span><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> = 
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_17"><span class="lab"><font color="Green" title="E34">A63</font></span></a>, <a class="ref" href="cat_7.html#T9" onmouseover="rs('cat_7/T9')" onmouseout="rh()">CAT_7:9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19_1_1_1_5_5_17"><span class="lab"><font color="Green" title="E35">A64</font></span></a>, <a class="ref" href="cat_7.html#T9" onmouseover="rs('cat_7/T9')" onmouseout="rh()">CAT_7:9</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="19_1_1_1_5_5_18"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_18"/><span class="lab"><font color="Green" title="E34">A65</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A66</font></span>: 
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c3">f2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:19_1_1_1_5"><span class="lab"><font color="Green" title="E32">A34</font></span></a>, <a class="txt" href="#E5:19_1_1_1_5"><span class="lab"><font color="Green" title="E33">A37</font></span></a></span>;<br/><a NAME="E3:19_1_1_1_5_5_18"/><span class="kw">then </span>
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c3">f2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_5_5_18"/>
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19_1_1_1_5_5_18"><span class="lab"><font color="Green" title="E35">A66</font></span></a>, <a class="ref" href="cat_7.html#T9" onmouseover="rs('cat_7/T9')" onmouseout="rh()">CAT_7:9</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"> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span></span><br/><a NAME="E5:19_1_1_1_5_5_18"/><span class="lab"><font color="Green" title="E36">A67</font></span>: 
 <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c2">f1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><a NAME="E6:19_1_1_1_5_5_18"/>
 <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> = 
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_18"><span class="lab"><font color="Green" title="E34">A65</font></span></a>, <a class="ref" href="cat_7.html#T9" onmouseover="rs('cat_7/T9')" onmouseout="rh()">CAT_7:9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19_1_1_1_5_5_18"><span class="lab"><font color="Green" title="E35">A66</font></span></a>, <a class="ref" href="cat_7.html#T9" onmouseover="rs('cat_7/T9')" onmouseout="rh()">CAT_7:9</a>, <a class="txt" href="#E5:19_1_1_1_5_5_18"><span class="lab"><font color="Green" title="E36">A67</font></span></a></span>
;<br/> <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="19_1_1_1_5_5_19"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_19"/><span class="lab"><font color="Green" title="E34">A68</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_19"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A69</font></span>: 
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c3">f2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19_1_1_1_5"><span class="lab"><font color="Green" title="E30">A28</font></span></a>, <a class="txt" href="#E7:19_1_1_1"><span class="lab"><font color="Green" title="E27">A21</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_5_5_19"/>
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_7.html#T8" onmouseover="rs('cat_7/T8')" onmouseout="rh()">CAT_7:8</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"> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span></span><br/><span class="kw">thus </span><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> = 
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_19"><span class="lab"><font color="Green" title="E34">A68</font></span></a>, <a class="ref" href="cat_7.html#T8" onmouseover="rs('cat_7/T8')" onmouseout="rh()">CAT_7:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19_1_1_1_5_5_19"><span class="lab"><font color="Green" title="E35">A69</font></span></a>, <a class="ref" href="cat_7.html#T8" onmouseover="rs('cat_7/T8')" onmouseout="rh()">CAT_7:8</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="19_1_1_1_5_5_20"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_20"/><span class="lab"><font color="Green" title="E34">A70</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_20"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a>, <a class="ref" href="cat_6.html#T26" onmouseover="rs('cat_6/T26')" onmouseout="rh()">CAT_6:26</a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_5_5_20"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_20"><span class="lab"><font color="Green" title="E34">A70</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_21"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_21"/><span class="lab"><font color="Green" title="E34">A71</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_21"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a>, <a class="ref" href="cat_6.html#T26" onmouseover="rs('cat_6/T26')" onmouseout="rh()">CAT_6:26</a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_5_5_21"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_21"><span class="lab"><font color="Green" title="E34">A71</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_22"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_22"/><span class="lab"><font color="Green" title="E34">A72</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_22"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c8">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_5_5_22"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_22"><span class="lab"><font color="Green" title="E34">A72</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_23"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_23"/><span class="lab"><font color="Green" title="E34">A73</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_23"/>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_5_5_23"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_23"><span class="lab"><font color="Green" title="E34">A73</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_24"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_24"/><span class="lab"><font color="Green" title="E34">A74</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_24"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><a NAME="E3:19_1_1_1_5_5_24"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_5_5_24"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_24"><span class="lab"><font color="Green" title="E34">A74</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_25"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_25"/><span class="lab"><font color="Green" title="E34">A75</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_25"/>
 <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_25"><span class="lab"><font color="Green" title="E34">A75</font></span></a>, <a class="txt" href="#E2:19_1_1"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a>, <a class="ref" href="cat_6.html#T26" onmouseover="rs('cat_6/T26')" onmouseout="rh()">CAT_6:26</a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_5_5_25"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_26"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_26"/><span class="lab"><font color="Green" title="E34">A76</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A77</font></span>: 
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c3">f2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:19_1_1_1_5"><span class="lab"><font color="Green" title="E31">A31</font></span></a>, <a class="txt" href="#E8:19_1_1_1"><span class="lab"><font color="Green" title="E28">A24</font></span></a></span>;<br/><a NAME="E3:19_1_1_1_5_5_26"/><span class="kw">then </span>
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a></span>;<br/><a NAME="E4:19_1_1_1_5_5_26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A78</font></span>: 
 <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c3">f2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19_1_1_1_5_5_26"><span class="lab"><font color="Green" title="E35">A77</font></span></a>, <a class="ref" href="cat_7.html#T6" onmouseover="rs('cat_7/T6')" onmouseout="rh()">CAT_7:6</a></span>;<br/><a NAME="E5:19_1_1_1_5_5_26"/>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:19_1_1_1_5_5_26"><span class="lab"><font color="Green" title="E36">A78</font></span></a>, <a class="txt" href="#E2:19_1_1_1_5_5_26"><span class="lab"><font color="Green" title="E35">A77</font></span></a>, <a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><span class="kw">hence </span><a NAME="E6:19_1_1_1_5_5_26"/><span class="lab"><font color="Green" title="E37">A79</font></span>: 
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</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"> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span></span><br/><span class="kw">thus </span><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> = 
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_26"><span class="lab"><font color="Green" title="E34">A76</font></span></a>, <a class="ref" href="cat_7.html#T8" onmouseover="rs('cat_7/T8')" onmouseout="rh()">CAT_7:8</a>, <a class="txt" href="#E2:19_1_1"><span class="lab"><font color="Green" title="E18">A2</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1_1_5_5_26"><span class="lab"><font color="Green" title="E37">A79</font></span></a>, <a class="txt" href="#E2:19_1_1_1_5_5_26"><span class="lab"><font color="Green" title="E35">A77</font></span></a>, <a class="ref" href="cat_6.html#T23" onmouseover="rs('cat_6/T23')" onmouseout="rh()">CAT_6:23</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="19_1_1_1_5_5_27"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_27"/><span class="lab"><font color="Green" title="E34">A80</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_27"/>
 <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_27"><span class="lab"><font color="Green" title="E34">A80</font></span></a>, <a class="txt" href="#E2:19_1_1"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a>, <a class="ref" href="cat_6.html#T26" onmouseover="rs('cat_6/T26')" onmouseout="rh()">CAT_6:26</a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_5_5_27"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_28"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_28"/><span class="lab"><font color="Green" title="E34">A81</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A82</font></span>: 
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:19_1_1_1"><span class="lab"><font color="Green" title="E27">A21</font></span></a>, <a class="txt" href="#E8:19_1_1_1"><span class="lab"><font color="Green" title="E28">A24</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_5_5_28"/>
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E17">A1</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"> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span></span><br/><span class="kw">thus </span><a NAME="E4:19_1_1_1_5_5_28"/>
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19_1_1_1_5"><span class="lab"><font color="Green" title="E33">A37</font></span></a>, <a class="txt" href="#E2:19_1_1_1_5_5_28"><span class="lab"><font color="Green" title="E35">A82</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5_5_28"><span class="lab"><font color="Green" title="E34">A81</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="19_1_1_1_5_5_29"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_29"/><span class="lab"><font color="Green" title="E34">A83</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_29"/>
 <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_29"><span class="lab"><font color="Green" title="E34">A83</font></span></a>, <a class="txt" href="#E2:19_1_1"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_5_5_29"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_30"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_30"/><span class="lab"><font color="Green" title="E34">A84</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_30"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><a NAME="E3:19_1_1_1_5_5_30"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_5_5_30"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_30"><span class="lab"><font color="Green" title="E34">A84</font></span></a>, <a class="txt" href="#E2:19_1_1"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_31"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_31"/><span class="lab"><font color="Green" title="E34">A85</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_31"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A86</font></span>: 
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c3">f2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c3">f2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19_1_1_1_5"><span class="lab"><font color="Green" title="E30">A28</font></span></a>, <a class="txt" href="#E5:19_1_1_1_5"><span class="lab"><font color="Green" title="E33">A37</font></span></a></span>;<br/><a NAME="E3:19_1_1_1_5_5_31"/><span class="lab"><font color="Green" title="E36">A87</font></span>: 
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c3">f2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_5_5_31"/>
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19_1_1_1_5_5_31"><span class="lab"><font color="Green" title="E35">A86</font></span></a>, <a class="ref" href="cat_7.html#T8" onmouseover="rs('cat_7/T8')" onmouseout="rh()">CAT_7:8</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"> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span></span><br/><a NAME="E5:19_1_1_1_5_5_31"/>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><a NAME="E6:19_1_1_1_5_5_31"/><span class="kw">then </span>
<font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_31"><span class="lab"><font color="Green" title="E34">A85</font></span></a>, <a class="ref" href="cat_7.html#T8" onmouseover="rs('cat_7/T8')" onmouseout="rh()">CAT_7:8</a></span>;<br/><span class="kw">hence </span><a NAME="E7:19_1_1_1_5_5_31"/>
<font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_31"><span class="lab"><font color="Green" title="E34">A85</font></span></a>, <a class="txt" href="#E3:19_1_1_1_5_5_31"><span class="lab"><font color="Green" title="E36">A87</font></span></a>, <a class="txt" href="#E2:19_1_1_1_5_5_31"><span class="lab"><font color="Green" title="E35">A86</font></span></a>, <a class="ref" href="cat_7.html#T8" onmouseover="rs('cat_7/T8')" onmouseout="rh()">CAT_7:8</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="19_1_1_1_5_5_32"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_32"/><span class="lab"><font color="Green" title="E34">A88</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_32"/>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_32"><span class="lab"><font color="Green" title="E34">A88</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a>, <a class="ref" href="cat_6.html#T26" onmouseover="rs('cat_6/T26')" onmouseout="rh()">CAT_6:26</a></span>;<br/><a NAME="E3:19_1_1_1_5_5_32"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5_5_32"><span class="lab"><font color="Green" title="E34">A88</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_5_5_32"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_33"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_33"/><span class="lab"><font color="Green" title="E34">A89</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_33"/>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_33"><span class="lab"><font color="Green" title="E34">A89</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a>, <a class="ref" href="cat_6.html#T26" onmouseover="rs('cat_6/T26')" onmouseout="rh()">CAT_6:26</a></span>;<br/><a NAME="E3:19_1_1_1_5_5_33"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5_5_33"><span class="lab"><font color="Green" title="E34">A89</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_5_5_33"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_34"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_34"/><span class="lab"><font color="Green" title="E34">A90</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_34"/>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_34"><span class="lab"><font color="Green" title="E34">A90</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><a NAME="E3:19_1_1_1_5_5_34"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5_5_34"><span class="lab"><font color="Green" title="E34">A90</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_5_5_34"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_35"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_35"/><span class="lab"><font color="Green" title="E34">A91</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_35"/>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5_5_35"><span class="lab"><font color="Green" title="E34">A91</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><a NAME="E3:19_1_1_1_5_5_35"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5_5_35"><span class="lab"><font color="Green" title="E34">A91</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_5_5_35"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_5_5_36"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_5_5_36"/><span class="lab"><font color="Green" title="E34">A92</font></span>: 
( <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</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"> ( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:19_1_1_1_5_5_36"/>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c9">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_5"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><a NAME="E3:19_1_1_1_5_5_36"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5_5_36"><span class="lab"><font color="Green" title="E34">A92</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><a NAME="E4:19_1_1_1_5_5_36"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E1:19_1_1_1_5_5_36"><span class="lab"><font color="Green" title="E34">A92</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E5:19_1_1_1_5_5_36"/>
( <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font> &amp; <font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c8">g1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">F</font> = <font color="Maroon" title="c7">F</font> as   <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>,<font color="Maroon" title="c1">C</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1_1"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="ref" href="cat_6.html#D23" onmouseover="rs('cat_6/D23')" onmouseout="rh()">CAT_6:def 23</a>, <a class="ref" href="cat_6.html#D25" onmouseover="rs('cat_6/D25')" onmouseout="rh()">CAT_6:def 25</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c8">F</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">  for <font color="Olive" title="b1">g1</font>, <font color="Olive" title="b2">g2</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b1">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Olive" title="b2">g2</font> &amp;  not <font color="Olive" title="b1">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp;  not <font color="Olive" title="b2">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  holds <br/>( <font color="Maroon" title="c8">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b1">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c8">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b2">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c9">g1</font>, <font color="Maroon" title="c10">g2</font> be   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</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"> ( <font color="Maroon" title="c9">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c10">g2</font> &amp;  not <font color="Maroon" title="c9">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp;  not <font color="Maroon" title="c10">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  implies ( <font color="Maroon" title="c8">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c8">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> ) )</span><br/>

<span class="kw">assume </span><a NAME="E11:19_1_1_1"/><span class="lab"><font color="Green" title="E29">A93</font></span>: 
<font color="Maroon" title="c9">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Maroon" title="c10">g2</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"> ( <font color="Maroon" title="c9">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  or <font color="Maroon" title="c10">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  or ( <font color="Maroon" title="c8">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c8">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> ) )</span><br/>

<span class="kw">assume </span><a NAME="E12:19_1_1_1"/><span class="lab"><font color="Green" title="E30">A94</font></span>: 
(  not <font color="Maroon" title="c9">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp;  not <font color="Maroon" title="c10">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</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="c8">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c8">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> )</span><br/>

<a NAME="E13:19_1_1_1"/><span class="lab"><font color="Green" title="E31">A95</font></span>: 
( <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> or <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> or <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> or <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> or <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> or <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:19_1_1"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="ref" href="enumset1.html#D4" onmouseover="rs('enumset1/D4')" onmouseout="rh()">ENUMSET1:def 4</a></span>;<br/>
<a NAME="E14:19_1_1_1"/><span class="lab"><font color="Green" title="E32">A96</font></span>: 
( <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> or <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> or <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> or <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> or <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> or <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:19_1_1"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="ref" href="enumset1.html#D4" onmouseover="rs('enumset1/D4')" onmouseout="rh()">ENUMSET1:def 4</a></span>;<br/>
<a NAME="E15:19_1_1_1"/><span class="lab"><font color="Green" title="E33">A97</font></span>: 
( <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:19_1_1_1_6"/><span class="lab"><font color="Green" title="E34">A98</font></span>: 
( <font color="Maroon" title="c9">g1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">h1</font> or <font color="Maroon" title="c10">g2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">h2</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"> contradiction</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_6_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="E1:19_1_1_1_6_1"/>
( <font color="Maroon" title="c9">g1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">h1</font> or <font color="Maroon" title="c10">g2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">h2</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_6"><span class="lab"><font color="Green" title="E34">A98</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_6_1_1"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_6_1_1"/><span class="lab"><font color="Green" title="E35">A99</font></span>: 
<font color="Maroon" title="c9">g1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">h1</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"> contradiction</span><br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_6_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="E1:19_1_1_1_6_1_1_1"/>
( ( <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> ) or ( <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> ) or ( <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_6_1_1"><span class="lab"><font color="Green" title="E35">A99</font></span></a>, <a class="txt" href="#E13:19_1_1_1"><span class="lab"><font color="Green" title="E31">A95</font></span></a>, <a class="txt" href="#E14:19_1_1_1"><span class="lab"><font color="Green" title="E32">A96</font></span></a>, <a class="txt" href="#E12:19_1_1_1"><span class="lab"><font color="Green" title="E30">A94</font></span></a>, <a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_6_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_6_1_1_1_1"/><span class="lab"><font color="Green" title="E36">A100</font></span>: 
( <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</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"> contradiction</span><br/><div class="add"><a NAME="E2:19_1_1_1_6_1_1_1_1"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c9">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:19_1_1_1"><span class="lab"><font color="Green" title="E29">A93</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_6_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_6_1_1_1_1"><span class="lab"><font color="Green" title="E36">A100</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_6_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_6_1_1_1_2"/><span class="lab"><font color="Green" title="E36">A101</font></span>: 
( <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</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"> contradiction</span><br/><div class="add"><a NAME="E2:19_1_1_1_6_1_1_1_2"/>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c10">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:19_1_1_1"><span class="lab"><font color="Green" title="E29">A93</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_6_1_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_6_1_1_1_2"><span class="lab"><font color="Green" title="E36">A101</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_6_1_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_6_1_1_1_3"/><span class="lab"><font color="Green" title="E36">A102</font></span>: 
( <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</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"> contradiction</span><br/><div class="add"><a NAME="E2:19_1_1_1_6_1_1_1_3"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:19_1_1_1"><span class="lab"><font color="Green" title="E29">A93</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><a NAME="E3:19_1_1_1_6_1_1_1_3"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_6_1_1_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_6_1_1_1_3"><span class="lab"><font color="Green" title="E36">A102</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_6_1_1_1_4"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_6_1_1_1_4"/><span class="lab"><font color="Green" title="E36">A103</font></span>: 
( <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</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"> contradiction</span><br/><div class="add"><a NAME="E2:19_1_1_1_6_1_1_1_4"/>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_6_1_1_1_4"><span class="lab"><font color="Green" title="E36">A103</font></span></a>, <a class="txt" href="#E11:19_1_1_1"><span class="lab"><font color="Green" title="E29">A93</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><a NAME="E3:19_1_1_1_6_1_1_1_4"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E1:19_1_1_1_6_1_1_1_4"><span class="lab"><font color="Green" title="E36">A103</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_6_1_1_1_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_6_1_1_1_5"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_6_1_1_1_5"/><span class="lab"><font color="Green" title="E36">A104</font></span>: 
( <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</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"> contradiction</span><br/><div class="add"><a NAME="E2:19_1_1_1_6_1_1_1_5"/>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_6_1_1_1_5"><span class="lab"><font color="Green" title="E36">A104</font></span></a>, <a class="txt" href="#E11:19_1_1_1"><span class="lab"><font color="Green" title="E29">A93</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><a NAME="E3:19_1_1_1_6_1_1_1_5"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E1:19_1_1_1_6_1_1_1_5"><span class="lab"><font color="Green" title="E36">A104</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_6_1_1_1_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_6_1_1_1_6"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_6_1_1_1_6"/><span class="lab"><font color="Green" title="E36">A105</font></span>: 
( <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</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"> contradiction</span><br/><div class="add"><a NAME="E2:19_1_1_1_6_1_1_1_6"/>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c10">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:19_1_1_1"><span class="lab"><font color="Green" title="E29">A93</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><a NAME="E3:19_1_1_1_6_1_1_1_6"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E1:19_1_1_1_6_1_1_1_6"><span class="lab"><font color="Green" title="E36">A105</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><a NAME="E4:19_1_1_1_6_1_1_1_6"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E1:19_1_1_1_6_1_1_1_6"><span class="lab"><font color="Green" title="E36">A105</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E5:19_1_1_1_6_1_1_1_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_6_1_2"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_6_1_2"/><span class="lab"><font color="Green" title="E35">A106</font></span>: 
<font color="Maroon" title="c10">g2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">h2</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"> contradiction</span><br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_6_1_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="E1:19_1_1_1_6_1_2_1"/>
( ( <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> ) or ( <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> ) or ( <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> ) or ( <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_6_1_2"><span class="lab"><font color="Green" title="E35">A106</font></span></a>, <a class="txt" href="#E13:19_1_1_1"><span class="lab"><font color="Green" title="E31">A95</font></span></a>, <a class="txt" href="#E14:19_1_1_1"><span class="lab"><font color="Green" title="E32">A96</font></span></a>, <a class="txt" href="#E12:19_1_1_1"><span class="lab"><font color="Green" title="E30">A94</font></span></a>, <a class="ref" href="cat_6.html#T22" onmouseover="rs('cat_6/T22')" onmouseout="rh()">CAT_6:22</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_6_1_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_6_1_2_1_1"/><span class="lab"><font color="Green" title="E36">A107</font></span>: 
( <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</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"> contradiction</span><br/><div class="add"><a NAME="E2:19_1_1_1_6_1_2_1_1"/>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c10">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:19_1_1_1"><span class="lab"><font color="Green" title="E29">A93</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_6_1_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_6_1_2_1_1"><span class="lab"><font color="Green" title="E36">A107</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_6_1_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_6_1_2_1_2"/><span class="lab"><font color="Green" title="E36">A108</font></span>: 
( <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</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"> contradiction</span><br/><div class="add"><a NAME="E2:19_1_1_1_6_1_2_1_2"/>
 <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_6_1_2_1_2"><span class="lab"><font color="Green" title="E36">A108</font></span></a>, <a class="txt" href="#E2:19_1_1"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E11:19_1_1_1"><span class="lab"><font color="Green" title="E29">A93</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><span class="kw">hence </span><a NAME="E3:19_1_1_1_6_1_2_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_6_1_2_1_3"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_6_1_2_1_3"/><span class="lab"><font color="Green" title="E36">A109</font></span>: 
( <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> &amp; <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</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"> contradiction</span><br/><div class="add"><a NAME="E2:19_1_1_1_6_1_2_1_3"/>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_6_1_2_1_3"><span class="lab"><font color="Green" title="E36">A109</font></span></a>, <a class="txt" href="#E11:19_1_1_1"><span class="lab"><font color="Green" title="E29">A93</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><a NAME="E3:19_1_1_1_6_1_2_1_3"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E1:19_1_1_1_6_1_2_1_3"><span class="lab"><font color="Green" title="E36">A109</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_6_1_2_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_6_1_2_1_4"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_6_1_2_1_4"/><span class="lab"><font color="Green" title="E36">A110</font></span>: 
( <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</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"> contradiction</span><br/><div class="add"><a NAME="E2:19_1_1_1_6_1_2_1_4"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:19_1_1_1"><span class="lab"><font color="Green" title="E29">A93</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><a NAME="E3:19_1_1_1_6_1_2_1_4"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_6_1_2_1_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_6_1_2_1_4"><span class="lab"><font color="Green" title="E36">A110</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_6_1_2_1_5"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_6_1_2_1_5"/><span class="lab"><font color="Green" title="E36">A111</font></span>: 
( <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</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"> contradiction</span><br/><div class="add"><a NAME="E2:19_1_1_1_6_1_2_1_5"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:19_1_1_1"><span class="lab"><font color="Green" title="E29">A93</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><a NAME="E3:19_1_1_1_6_1_2_1_5"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:19_1_1_1_6_1_2_1_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_1_6_1_2_1_5"><span class="lab"><font color="Green" title="E36">A111</font></span></a>, <a class="txt" href="#E2:19_1_1"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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="19_1_1_1_6_1_2_1_6"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_1_6_1_2_1_6"/><span class="lab"><font color="Green" title="E36">A112</font></span>: 
( <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> &amp; <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</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"> contradiction</span><br/><div class="add"><a NAME="E2:19_1_1_1_6_1_2_1_6"/>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c10">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:19_1_1_1"><span class="lab"><font color="Green" title="E29">A93</font></span></a>, <a class="ref" href="cat_7.html#T5" onmouseover="rs('cat_7/T5')" onmouseout="rh()">CAT_7:5</a></span>;<br/><a NAME="E3:19_1_1_1_6_1_2_1_6"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E1:19_1_1_1_6_1_2_1_6"><span class="lab"><font color="Green" title="E36">A112</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><a NAME="E4:19_1_1_1_6_1_2_1_6"/><span class="kw">then </span>
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E1:19_1_1_1_6_1_2_1_6"><span class="lab"><font color="Green" title="E36">A112</font></span></a>, <a class="ref" href="cat_7.html#T4" onmouseover="rs('cat_7/T4')" onmouseout="rh()">CAT_7:4</a></span>;<br/><span class="kw">hence </span><a NAME="E5:19_1_1_1_6_1_2_1_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" onmouseover="rs('zfmisc_1/D8')" onmouseout="rh()">ZFMISC_1:def 8</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></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="kw">thus </span><a NAME="E16:19_1_1_1"/>
( <font color="Maroon" title="c8">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c9">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c8">F</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c10">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:19_1_1_1"><span class="lab"><font color="Green" title="E27">A21</font></span></a>, <a class="txt" href="#E8:19_1_1_1"><span class="lab"><font color="Green" title="E28">A24</font></span></a>, <a class="txt" href="#E15:19_1_1_1"><span class="lab"><font color="Green" title="E33">A97</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>
<a NAME="E8:19_1_1"/><span class="lab"><font color="Green" title="E24">A113</font></span>: 
 for <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">F2</font> being   <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>,<font color="Maroon" title="c1">C</font>  st (  for <font color="Olive" title="b3">g1</font>, <font color="Olive" title="b4">g2</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b3">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Olive" title="b4">g2</font> &amp;  not <font color="Olive" title="b3">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp;  not <font color="Olive" title="b4">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  holds <br/>( <font color="Olive" title="b1">F1</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Olive" title="b1">F1</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b4">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> ) ) &amp; (  for <font color="Olive" title="b3">g1</font>, <font color="Olive" title="b4">g2</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b3">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Olive" title="b4">g2</font> &amp;  not <font color="Olive" title="b3">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp;  not <font color="Olive" title="b4">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  holds <br/>( <font color="Olive" title="b2">F2</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Olive" title="b2">F2</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b4">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> ) ) holds <br/><font color="Olive" title="b1">F1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">F2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="19_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">F1</font>, <font color="Maroon" title="c7">F2</font> be   <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>,<font color="Maroon" title="c1">C</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"> ( (  for <font color="Olive" title="b1">g1</font>, <font color="Olive" title="b2">g2</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b1">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Olive" title="b2">g2</font> &amp;  not <font color="Olive" title="b1">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp;  not <font color="Olive" title="b2">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  holds <br/>( <font color="Maroon" title="c6">F1</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b1">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c6">F1</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b2">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> ) ) &amp; (  for <font color="Olive" title="b1">g1</font>, <font color="Olive" title="b2">g2</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b1">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Olive" title="b2">g2</font> &amp;  not <font color="Olive" title="b1">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp;  not <font color="Olive" title="b2">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  holds <br/>( <font color="Maroon" title="c7">F2</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b1">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c7">F2</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b2">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> ) ) implies <font color="Maroon" title="c6">F1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">F2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:19_1_1_2"/><span class="lab"><font color="Green" title="E25">A114</font></span>: 
 for <font color="Olive" title="b1">g1</font>, <font color="Olive" title="b2">g2</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b1">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Olive" title="b2">g2</font> &amp;  not <font color="Olive" title="b1">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp;  not <font color="Olive" title="b2">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  holds <br/>( <font color="Maroon" title="c6">F1</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b1">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c6">F1</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b2">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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"> (  ex <font color="Olive" title="b1">g1</font>, <font color="Olive" title="b2">g2</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span> st <br/>( <font color="Olive" title="b1">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Olive" title="b2">g2</font> &amp;  not <font color="Olive" title="b1">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp;  not <font color="Olive" title="b2">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c7">F2</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b1">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c7">F2</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b2">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> ) ) or <font color="Maroon" title="c6">F1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">F2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:19_1_1_2"/><span class="lab"><font color="Green" title="E26">A115</font></span>: 
 for <font color="Olive" title="b1">g1</font>, <font color="Olive" title="b2">g2</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b1">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Olive" title="b2">g2</font> &amp;  not <font color="Olive" title="b1">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp;  not <font color="Olive" title="b2">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  holds <br/>( <font color="Maroon" title="c7">F2</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b1">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c7">F2</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b2">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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"> <font color="Maroon" title="c6">F1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">F2</font></span><br/>

<a NAME="E3:19_1_1_2"/>
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span> holds <br/><font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="19_1_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">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"> ( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span> implies <font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:19_1_1_2_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</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"> <font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span><br/>

<a NAME="E2:19_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A116</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2">(<span class="default"><a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font></span>)</span>,<font color="Maroon" title="c4">h2</font>,<font color="Maroon" title="c5">h1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font></span>)</span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:19_1_1"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="ref" href="cat_6.html#D1" onmouseover="rs('cat_6/D1')" onmouseout="rh()">CAT_6:def 1</a></span>;<br/>
<span class="lab"><font color="Green" title="E28">A117</font></span>: <font color="Maroon" title="c6">F1</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c5">h1</font> = 
<font color="Maroon" title="c2">f1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19_1_1"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E1:19_1_1_2"><span class="lab"><font color="Green" title="E25">A114</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c7">F2</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c5">h1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19_1_1"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E2:19_1_1_2"><span class="lab"><font color="Green" title="E26">A115</font></span></a></span>
;<br/>
<span class="lab"><font color="Green" title="E29">A118</font></span>: <font color="Maroon" title="c6">F1</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c4">h2</font> = 
<font color="Maroon" title="c3">f2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19_1_1"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E1:19_1_1_2"><span class="lab"><font color="Green" title="E25">A114</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c7">F2</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c4">h2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19_1_1"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E2:19_1_1_2"><span class="lab"><font color="Green" title="E26">A115</font></span></a></span>
;<br/>
<a NAME="E5:19_1_1_2_1"/><span class="lab"><font color="Green" title="E30">A119</font></span>: 
( <font color="Maroon" title="c6">F1</font> is  <a href="cat_6.html#V14" title="CAT_6:attr.14">multiplicative</a>  &amp; <font color="Maroon" title="c7">F2</font> is  <a href="cat_6.html#V14" title="CAT_6:attr.14">multiplicative</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D25" onmouseover="rs('cat_6/D25')" onmouseout="rh()">CAT_6:def 25</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_2_1_3"><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="E1:19_1_1_2_1_3"/>
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19_1_1_2_1"><span class="lab"><font color="Green" title="E27">A116</font></span></a>, <a class="ref" href="enumset1.html#D4" onmouseover="rs('enumset1/D4')" onmouseout="rh()">ENUMSET1:def 4</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_2_1_3_1"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_2_1_3_1"/><span class="lab"><font color="Green" title="E31">A120</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c4">h2</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"> <font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span><br/><div class="add"><span class="kw">hence </span><font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> = 
 <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F1</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c4">h2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#T32" onmouseover="rs('cat_6/T32')" onmouseout="rh()">CAT_6:32</a></span>
<br/>.= 
<font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_2_1_3_1"><span class="lab"><font color="Green" title="E31">A120</font></span></a>, <a class="txt" href="#E4:19_1_1_2_1"><span class="lab"><font color="Green" title="E29">A118</font></span></a>, <a class="ref" href="cat_6.html#T32" onmouseover="rs('cat_6/T32')" onmouseout="rh()">CAT_6:32</a></span>
;<br/> <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="19_1_1_2_1_3_2"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_2_1_3_2"/><span class="lab"><font color="Green" title="E31">A121</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c4">h2</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"> <font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span><br/><div class="add"><span class="kw">hence </span><font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> = 
 <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F1</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c4">h2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#T32" onmouseover="rs('cat_6/T32')" onmouseout="rh()">CAT_6:32</a></span>
<br/>.= 
<font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_2_1_3_2"><span class="lab"><font color="Green" title="E31">A121</font></span></a>, <a class="txt" href="#E4:19_1_1_2_1"><span class="lab"><font color="Green" title="E29">A118</font></span></a>, <a class="ref" href="cat_6.html#T32" onmouseover="rs('cat_6/T32')" onmouseout="rh()">CAT_6:32</a></span>
;<br/> <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="19_1_1_2_1_3_3"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_2_1_3_3"/><span class="lab"><font color="Green" title="E31">A122</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">h1</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"> <font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span><br/><div class="add"><span class="kw">hence </span><font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> = 
 <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F1</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c5">h1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#T32" onmouseover="rs('cat_6/T32')" onmouseout="rh()">CAT_6:32</a></span>
<br/>.= 
<font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_2_1_3_3"><span class="lab"><font color="Green" title="E31">A122</font></span></a>, <a class="txt" href="#E3:19_1_1_2_1"><span class="lab"><font color="Green" title="E28">A117</font></span></a>, <a class="ref" href="cat_6.html#T32" onmouseover="rs('cat_6/T32')" onmouseout="rh()">CAT_6:32</a></span>
;<br/> <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="19_1_1_2_1_3_4"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_2_1_3_4"/><span class="lab"><font color="Green" title="E31">A123</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h2</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"> <font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span><br/><div class="add"><span class="kw">hence </span><font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> = 
<font color="Maroon" title="c6">F1</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c4">h2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D21" onmouseover="rs('cat_6/D21')" onmouseout="rh()">CAT_6:def 21</a></span>
<br/>.= 
<font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_2_1_3_4"><span class="lab"><font color="Green" title="E31">A123</font></span></a>, <a class="txt" href="#E4:19_1_1_2_1"><span class="lab"><font color="Green" title="E29">A118</font></span></a>, <a class="ref" href="cat_6.html#D21" onmouseover="rs('cat_6/D21')" onmouseout="rh()">CAT_6:def 21</a></span>
;<br/> <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="19_1_1_2_1_3_5"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_2_1_3_5"/><span class="lab"><font color="Green" title="E31">A124</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</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"> <font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span><br/><div class="add"><span class="kw">hence </span><font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> = 
<font color="Maroon" title="c6">F1</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c5">h1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D21" onmouseover="rs('cat_6/D21')" onmouseout="rh()">CAT_6:def 21</a></span>
<br/>.= 
<font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_2_1_3_5"><span class="lab"><font color="Green" title="E31">A124</font></span></a>, <a class="txt" href="#E3:19_1_1_2_1"><span class="lab"><font color="Green" title="E28">A117</font></span></a>, <a class="ref" href="cat_6.html#D21" onmouseover="rs('cat_6/D21')" onmouseout="rh()">CAT_6:def 21</a></span>
;<br/> <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="19_1_1_2_1_3_6"><span class="kw">suppose </span></a><a NAME="E1:19_1_1_2_1_3_6"/><span class="lab"><font color="Green" title="E31">A125</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</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"> <font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span><br/><div class="add"><span class="kw">hence </span><font color="Maroon" title="c6">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> = 
<font color="Maroon" title="c6">F1</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#D21" onmouseover="rs('cat_6/D21')" onmouseout="rh()">CAT_6:def 21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">F2</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c5">h1</font></span>)</span> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F2</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Maroon" title="c4">h2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:19_1_1_2_1"><span class="lab"><font color="Green" title="E28">A117</font></span></a>, <a class="txt" href="#E4:19_1_1_2_1"><span class="lab"><font color="Green" title="E29">A118</font></span></a>, <a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E5:19_1_1_2_1"><span class="lab"><font color="Green" title="E30">A119</font></span></a>, <a class="ref" href="cat_6.html#D23" onmouseover="rs('cat_6/D23')" onmouseout="rh()">CAT_6:def 23</a></span>
<br/>.= 
<font color="Maroon" title="c7">F2</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Maroon" title="c4">h2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E5:19_1_1_2_1"><span class="lab"><font color="Green" title="E30">A119</font></span></a>, <a class="ref" href="cat_6.html#D23" onmouseover="rs('cat_6/D23')" onmouseout="rh()">CAT_6:def 23</a></span>
<br/>.= 
<font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1_2_1_3_6"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="ref" href="cat_6.html#D21" onmouseover="rs('cat_6/D21')" onmouseout="rh()">CAT_6:def 21</a></span>
;<br/> <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="E4:19_1_1_2"/>
<font color="Maroon" title="c6">F1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">F2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T12" onmouseover="rs('funct_2/T12')" onmouseout="rh()">FUNCT_2:12</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">thus </span><a NAME="E9:19_1_1"/>
(  ex <font color="Olive">b<sub>1</sub></font> being   <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>,<font color="Maroon" title="c1">C</font> st <br/> for <font color="Olive" title="b2">g1</font>, <font color="Olive" title="b3">g2</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b2">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Olive" title="b3">g2</font> &amp;  not <font color="Olive" title="b2">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp;  not <font color="Olive" title="b3">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b2">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b3">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> ) &amp; (  for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>,<font color="Maroon" title="c1">C</font>  st (  for <font color="Olive" title="b3">g1</font>, <font color="Olive" title="b4">g2</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b3">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Olive" title="b4">g2</font> &amp;  not <font color="Olive" title="b3">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp;  not <font color="Olive" title="b4">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b4">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> ) ) &amp; (  for <font color="Olive" title="b3">g1</font>, <font color="Olive" title="b4">g2</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 3</span>)</span>  st <font color="Olive" title="b3">g1</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Olive" title="b4">g2</font> &amp;  not <font color="Olive" title="b3">g1</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp;  not <font color="Olive" title="b4">g2</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  holds <br/>( <font color="Olive">b<sub>2</sub></font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b4">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> ) ) holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:19_1_1"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="txt" href="#E8:19_1_1"><span class="lab"><font color="Green" title="E24">A113</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>
