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

<span class="kw">set </span><font color="Maroon" title="c1">C</font> =  <a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 1;<br/>
<span class="kw">consider </span><font color="Maroon" title="c2">f</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> 1</span>)</span><span class="kw"> such that </span><br/><a NAME="E2:60"/><span class="lab"><font color="Green" title="E33">A1</font></span>: 
( <font color="Maroon" title="c2">f</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  &amp;  <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> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <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> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_8.html#T15" target="_self" onmouseover="rs('cat_8/T15')" onmouseout="rh()">Th15</a></span>;<br/>
<a NAME="E3:60"/><span class="lab"><font color="Green" title="E34">A2</font></span>: 
 for <font color="Olive" title="b1">o1</font>, <font color="Olive" title="b2">o2</font> being   <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> 1</span>)</span><br/>  for <font color="Olive" title="b3">f1</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> 1</span>)</span> holds  <font color="Olive" title="b3">f1</font> is    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Olive" title="b1">o1</font>,<font color="Olive" title="b2">o2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="60_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">o1</font>, <font color="Maroon" title="c4">o2</font> be   <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> 1</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">  for <font color="Olive" title="b1">f1</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> 1</span>)</span> holds  <font color="Olive" title="b1">f1</font> is    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c4">o2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">f1</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> 1</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="c5">f1</font> is    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c4">o2</font></span><br/>



<span class="lab"><font color="Green" title="E35">A3</font></span>:  <a href="cat_6.html#K6" title="CAT_6:func.6">dom</a> <font color="Maroon" title="c5">f1</font> = 
<font color="Maroon" title="c2">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c3">o1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>
;<br/>
 <a href="cat_6.html#K7" title="CAT_6:func.7">cod</a> <font color="Maroon" title="c5">f1</font> = 
<font color="Maroon" title="c2">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c4">o2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>
;<br/>
<a NAME="E3:60_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">f1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c4">o2</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:60_1"><span class="lab"><font color="Green" title="E35">A3</font></span></a>, <a class="ref" href="cat_7.html#T20" onmouseover="rs('cat_7/T20')" onmouseout="rh()">CAT_7:20</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:60_1"/>
<font color="Maroon" title="c5">f1</font> is    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c4">o2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_7.html#D3" onmouseover="rs('cat_7/D3')" onmouseout="rh()">CAT_7:def 3</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">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be   <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> 1</span>)</span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="cat_8.html#D11" target="_self" onmouseover="rs('cat_8/D11')" onmouseout="rh()">CAT_8:def 11</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">  ex <font color="Olive" title="b1">d</font> being   <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> 1</span>)</span> ex <font color="Olive" title="b2">p1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Olive" title="b1">d</font>,<font color="Maroon" title="c3">a</font> ex <font color="Olive" title="b3">p2</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Olive" title="b1">d</font>,<font color="Maroon" title="c4">b</font> st <br/>(  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Olive" title="b1">d</font>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Olive" title="b1">d</font>,<font color="Maroon" title="c4">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b1">d</font>,<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font> <a href="cat_8.html#R1" title="CAT_8:pred.1">is_product_of</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> )</span><br/>

<span class="lab"><font color="Green" title="E35">A4</font></span>: <font color="Maroon" title="c3">a</font> = 
<font color="Maroon" title="c2">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c4">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>
;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c3">a</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">p1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c3">a</font> ex <font color="Olive" title="b2">p2</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> st <br/>(  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">a</font>,<font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font> <a href="cat_8.html#R1" title="CAT_8:pred.1">is_product_of</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">p1</font> = <font color="Maroon" title="c2">f</font> as    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c3">a</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:60"><span class="lab"><font color="Green" title="E34">A2</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">p2</font> = <font color="Maroon" title="c2">f</font> as    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:60"><span class="lab"><font color="Green" title="E34">A2</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c5">p1</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">p2</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> st <br/>(  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">p1</font>,<font color="Olive" title="b1">p2</font> <a href="cat_8.html#R1" title="CAT_8:pred.1">is_product_of</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c6">p2</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font> <a href="cat_8.html#R1" title="CAT_8:pred.1">is_product_of</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> )</span><br/>

<span class="kw">thus </span><a NAME="E7:60"/><span class="lab"><font color="Green" title="E36">A5</font></span>: 
(  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:60"><span class="lab"><font color="Green" title="E35">A4</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="c3">a</font>,<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font> <a href="cat_8.html#R1" title="CAT_8:pred.1">is_product_of</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><br/>

<a NAME="E8:60"/>
 for <font color="Olive" title="b1">c1</font> being   <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> 1</span>)</span><br/>  for <font color="Olive" title="b2">q1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Olive" title="b1">c1</font>,<font color="Maroon" title="c3">a</font><br/>  for <font color="Olive" title="b3">q2</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Olive" title="b1">c1</font>,<font color="Maroon" title="c4">b</font>  st  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Olive" title="b1">c1</font>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Olive" title="b1">c1</font>,<font color="Maroon" title="c4">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/>(  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Olive" title="b1">c1</font>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  ex <font color="Olive" title="b4">h</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Olive" title="b1">c1</font>,<font color="Maroon" title="c3">a</font> st <br/>( <font color="Maroon" title="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">q2</font> &amp; (  for <font color="Olive" title="b5">h1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Olive" title="b1">c1</font>,<font color="Maroon" title="c3">a</font>  st <font color="Maroon" title="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b5">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b5">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">q2</font> holds <br/><font color="Olive" title="b4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">h1</font> ) ) )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="60_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c7">c1</font> be   <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> 1</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">  for <font color="Olive" title="b1">q1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font><br/>  for <font color="Olive" title="b2">q2</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c4">b</font>  st  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c4">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/>(  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  ex <font color="Olive" title="b3">h</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font> st <br/>( <font color="Maroon" title="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">q1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q2</font> &amp; (  for <font color="Olive" title="b4">h1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font>  st <font color="Maroon" title="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b4">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">q1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b4">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q2</font> holds <br/><font color="Olive" title="b3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">h1</font> ) ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c8">q1</font> be    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</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">q2</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c4">b</font>  st  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c4">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/>(  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  ex <font color="Olive" title="b2">h</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font> st <br/>( <font color="Maroon" title="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b2">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b2">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">q2</font> &amp; (  for <font color="Olive" title="b3">h1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font>  st <font color="Maroon" title="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b3">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b3">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">q2</font> holds <br/><font color="Olive" title="b2">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">h1</font> ) ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c9">q2</font> be    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c4">b</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c4">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies (  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  ex <font color="Olive" title="b1">h</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font> st <br/>( <font color="Maroon" title="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">q2</font> &amp; (  for <font color="Olive" title="b2">h1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font>  st <font color="Maroon" title="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b2">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b2">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">q2</font> holds <br/><font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">h1</font> ) ) ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:60_3"/>
(  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c4">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  ex <font color="Olive" title="b1">h</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font> st <br/>( <font color="Maroon" title="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">q2</font> &amp; (  for <font color="Olive" title="b2">h1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font>  st <font color="Maroon" title="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b2">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b2">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">q2</font> holds <br/><font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">h1</font> ) ) )</span><br/>

<font color="Maroon" title="c7">c1</font> = 
<font color="Maroon" title="c2">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c3">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:60_3"/>
 <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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">  ex <font color="Olive" title="b1">h</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font> st <br/>( <font color="Maroon" title="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">q2</font> &amp; (  for <font color="Olive" title="b2">h1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font>  st <font color="Maroon" title="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b2">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b2">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">q2</font> holds <br/><font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">h1</font> ) )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c10">h</font> = <font color="Maroon" title="c2">f</font> as    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:60"><span class="lab"><font color="Green" title="E34">A2</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c10">h</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="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c10">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c10">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">q2</font> &amp; (  for <font color="Olive" title="b1">h1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font>  st <font color="Maroon" title="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b1">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b1">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">q2</font> holds <br/><font color="Maroon" title="c10">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h1</font> ) )</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c10">h</font> = 
<font color="Maroon" title="c2">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c8">q1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI: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" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c10">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">q2</font> &amp; (  for <font color="Olive" title="b1">h1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font>  st <font color="Maroon" title="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b1">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b1">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">q2</font> holds <br/><font color="Maroon" title="c10">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h1</font> ) )</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c10">h</font> = 
<font color="Maroon" title="c2">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c9">q2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI: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">  for <font color="Olive" title="b1">h1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</font>  st <font color="Maroon" title="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b1">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b1">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">q2</font> holds <br/><font color="Maroon" title="c10">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h1</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c11">h1</font> be    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c7">c1</font>,<font color="Maroon" title="c3">a</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="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c11">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c11">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">q2</font> implies <font color="Maroon" title="c10">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">h1</font> )</span><br/>

<span class="kw">assume </span><a NAME="E7:60_3"/>
( <font color="Maroon" title="c5">p1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c11">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c11">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">q2</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="c10">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">h1</font></span><br/>

<span class="kw">thus </span><a NAME="E8:60_3"/>
<font color="Maroon" title="c10">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">h1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI: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>
<span class="kw">hence </span><a NAME="E9:60"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font> <a href="cat_8.html#R1" title="CAT_8:pred.1">is_product_of</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:60"><span class="lab"><font color="Green" title="E36">A5</font></span></a>, <a class="ref" href="cat_8.html#D10" target="_self" onmouseover="rs('cat_8/D10')" onmouseout="rh()">Def10</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>
