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

<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">o1</font>, <font color="Olive" title="b2">o2</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font><br/> for <font color="Olive" title="b3">m</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">o1</font>,<font color="Olive" title="b2">o2</font>  st <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b1">o1</font>,<font color="Olive" title="b2">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b2">o2</font>,<font color="Olive" title="b1">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b3">m</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a> holds <br/><font color="Olive" title="b3">m</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a>  is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a></span><br/><b>let </b><font color="Maroon" title="c2">o1</font>, <font color="Maroon" title="c3">o2</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">m</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c3">o2</font>  st <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c3">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c2">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b1">m</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a> holds <br/><font color="Olive" title="b1">m</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a>  is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a></span><br/><b>let </b><font color="Maroon" title="c4">m</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c3">o2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c3">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c2">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">m</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a> implies <font color="Maroon" title="c4">m</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a>  is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a> )</span><br/>







<b>assume </b><a NAME="E1:4"/><i><font color="Green" title="E4">A1</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c3">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c2">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">m</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a> or <font color="Maroon" title="c4">m</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a>  is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a> )</span><br/>

<b>assume </b><a NAME="E2:4"/>
<font color="Maroon" title="c4">m</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">m</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a>  is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a></span><br/>

<a NAME="E3:4"/><b>then </b><i><font color="Green" title="E5">A2</font></i>: 
( <font color="Maroon" title="c4">m</font> is <a href="altcat_3.html#V1" title="ALTCAT_3:attr.1">retraction</a> &amp; <font color="Maroon" title="c4">m</font> is <a href="altcat_3.html#V2" title="ALTCAT_3:attr.2">coretraction</a> )
 
<b>by </b><i><a class="ref" href="altcat_3.html#T5" title="ALTCAT_3:th.5">ALTCAT_3:5</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c4">m</font>
<b>by </b><i><a class="txt" href="#E1:4"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="altcat_3.html#T3" title="ALTCAT_3:th.3">ALTCAT_3:3</a></i>
<br/>.= 
 <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c2">o1</font>
<b>by </b><i><a class="txt" href="#E1:4"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="#E3:4"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="altcat_3.html#T2" title="ALTCAT_3:th.2">ALTCAT_3:2</a></i>
;<br/> <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_3.html#D5" title="ALTCAT_3:def.5">ALTCAT_3:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c3">o2</font></span><br/>

<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span> = 
<font color="Maroon" title="c4">m</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E1:4"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="#E3:4"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="altcat_3.html#T3" title="ALTCAT_3:th.3">ALTCAT_3:3</a></i>
<br/>.= 
 <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c3">o2</font>
<b>by </b><i><a class="txt" href="#E1:4"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="#E3:4"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="altcat_3.html#T2" title="ALTCAT_3:th.2">ALTCAT_3:2</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
