<?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>, <font color="Olive" title="b3">o3</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b1">o1</font>,<font color="Olive" title="b2">o2</font> <a href="altcat_3.html#R2" title="ALTCAT_3:pred.2">are_iso</a>  &amp; <font color="Olive" title="b2">o2</font>,<font color="Olive" title="b3">o3</font> <a href="altcat_3.html#R2" title="ALTCAT_3:pred.2">are_iso</a>  holds <br/><font color="Olive" title="b1">o1</font>,<font color="Olive" title="b3">o3</font> <a href="altcat_3.html#R2" title="ALTCAT_3:pred.2">are_iso</a> </span><br/><b>let </b><font color="Maroon" title="c2">o1</font>, <font color="Maroon" title="c3">o2</font>, <font color="Maroon" title="c4">o3</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"> ( <font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c3">o2</font> <a href="altcat_3.html#R2" title="ALTCAT_3:pred.2">are_iso</a>  &amp; <font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c4">o3</font> <a href="altcat_3.html#R2" title="ALTCAT_3:pred.2">are_iso</a>  implies <font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c4">o3</font> <a href="altcat_3.html#R2" title="ALTCAT_3:pred.2">are_iso</a>  )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:15"/><i><font color="Green" title="E14">A1</font></i>: 
<font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c3">o2</font> <a href="altcat_3.html#R2" title="ALTCAT_3:pred.2">are_iso</a> 
 <b>and </b><br/><a NAME="E2:15"/><i><font color="Green" title="E15">A2</font></i>: 
<font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c4">o3</font> <a href="altcat_3.html#R2" title="ALTCAT_3:pred.2">are_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="c2">o1</font>,<font color="Maroon" title="c4">o3</font> <a href="altcat_3.html#R2" title="ALTCAT_3:pred.2">are_iso</a> </span><br/>

<a NAME="E3:15"/><i><font color="Green" title="E16">A3</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>  &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="c4">o3</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="c4">o3</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>  )
 
<b>by </b><i><a class="txt" href="#E1:15"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="#E2:15"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="altcat_3.html#D6" target="_self" title="ALTCAT_3:def.6">Def6</a></i>;<br/>
<b>hence </b><a NAME="E4:15"/><i><font color="Green" title="E17">A4</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="c4">o3</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="c4">o3</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>  )
 <b>by </b><i><a class="ref" href="altcat_1.html#D4" title="ALTCAT_1:def.4">ALTCAT_1:def 4</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_3.html#D6" target="_self" title="ALTCAT_3:def.6">ALTCAT_3:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">A</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="c4">o3</font> st <font color="Olive" title="b1">A</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a></span><br/>

<b>consider </b><font color="Maroon" title="c5">A</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><b> such that </b><br/><a NAME="E6:15"/><i><font color="Green" title="E18">A5</font></i>: 
<font color="Maroon" title="c5">A</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a>
 <b>by </b><i><a class="txt" href="#E1:15"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="altcat_3.html#D6" target="_self" title="ALTCAT_3:def.6">Def6</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">B</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c4">o3</font><b> such that </b><br/><a NAME="E8:15"/><i><font color="Green" title="E19">A6</font></i>: 
<font color="Maroon" title="c6">B</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a>
 <b>by </b><i><a class="txt" href="#E2:15"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="altcat_3.html#D6" target="_self" title="ALTCAT_3:def.6">Def6</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">B</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">A</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">B</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">A</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a></span><br/>

<b>thus </b><a NAME="E9:15"/>
<font color="Maroon" title="c6">B</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">A</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a>
 <b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E16">A3</font></i></a>, <a class="txt" href="#E4:15"><i><font color="Green" title="E17">A4</font></i></a>, <a class="txt" href="#E6:15"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="#E8:15"><i><font color="Green" title="E19">A6</font></i></a>, <a class="ref" href="altcat_3.html#T7" target="_self" title="ALTCAT_3:th.7">Th7</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>
