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<b>let </b><font color="Maroon" title="c4">o1</font>, <font color="Maroon" title="c5">o2</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:14_1_2"/><i><font color="Green" title="E13">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="c4">o1</font>,<font color="Maroon" title="c5">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="c5">o2</font>,<font color="Maroon" title="c4">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>and </b><br/><a NAME="E2:14_1_2"/><i><font color="Green" title="E14">A4</font></i>: 
 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="c4">o1</font>,<font color="Maroon" title="c5">o2</font> st <font color="Olive" title="b1">A</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a>
 ;<br/>

<b>consider </b><font color="Maroon" title="c6">A</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c5">o2</font><b> such that </b><br/><a NAME="E4:14_1_2"/><i><font color="Green" title="E15">A5</font></i>: 
<font color="Maroon" title="c6">A</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a>
 <b>by </b><i><a class="txt" href="altcat_3.html#E2:14_1_2"><i><font color="Green" title="E14">A4</font></i></a></i>;<br/>
<a NAME="E5:14_1_2"/><i><font color="Green" title="E16">A6</font></i>: 
( <font color="Maroon" title="c6">A</font> is <a href="altcat_3.html#V1" title="ALTCAT_3:attr.1">retraction</a> &amp; <font color="Maroon" title="c6">A</font> is <a href="altcat_3.html#V2" title="ALTCAT_3:attr.2">coretraction</a> )
 
<b>by </b><i><a class="txt" href="altcat_3.html#E4:14_1_2"><i><font color="Green" title="E15">A5</font></i></a>, <a class="ref" href="altcat_3.html#T5" target="_self" title="ALTCAT_3:th.5">Th5</a></i>;<br/>
<b>thus </b><a NAME="E6:14_1_2"/>
( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">o2</font>,<font color="Maroon" title="c4">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="c4">o1</font>,<font color="Maroon" title="c5">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="altcat_3.html#E1:14_1_2"><i><font color="Green" title="E13">A3</font></i></a></i>;<br/>

<b>take </b><font color="Maroon" title="c7">A1</font> = <font color="Maroon" title="c6">A</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> ;<br/>

<i><font color="Green" title="E17">A7</font></i>: <font color="Maroon" title="c7">A1</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">A1</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">A</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="c6">A</font>
<b>by </b><i><a class="txt" href="altcat_3.html#E1:14_1_2"><i><font color="Green" title="E13">A3</font></i></a>, <a class="txt" href="altcat_3.html#E5:14_1_2"><i><font color="Green" title="E16">A6</font></i></a>, <a class="ref" href="altcat_3.html#T3" target="_self" title="ALTCAT_3:th.3">Th3</a></i>
<br/>.= 
 <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c4">o1</font>
<b>by </b><i><a class="txt" href="altcat_3.html#E1:14_1_2"><i><font color="Green" title="E13">A3</font></i></a>, <a class="txt" href="altcat_3.html#E5:14_1_2"><i><font color="Green" title="E16">A6</font></i></a>, <a class="ref" href="altcat_3.html#T2" target="_self" title="ALTCAT_3:th.2">Th2</a></i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c7">A1</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="c7">A1</font> = 
<font color="Maroon" title="c6">A</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">A</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="altcat_3.html#E1:14_1_2"><i><font color="Green" title="E13">A3</font></i></a>, <a class="txt" href="altcat_3.html#E5:14_1_2"><i><font color="Green" title="E16">A6</font></i></a>, <a class="ref" href="altcat_3.html#T3" target="_self" title="ALTCAT_3:th.3">Th3</a></i>
<br/>.= 
 <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c5">o2</font>
<b>by </b><i><a class="txt" href="altcat_3.html#E1:14_1_2"><i><font color="Green" title="E13">A3</font></i></a>, <a class="txt" href="altcat_3.html#E5:14_1_2"><i><font color="Green" title="E16">A6</font></i></a>, <a class="ref" href="altcat_3.html#T2" target="_self" title="ALTCAT_3:th.2">Th2</a></i>
;<br/>
<b>hence </b><a NAME="E9:14_1_2"/>
<font color="Maroon" title="c7">A1</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a>
 <b>by </b><i><a class="txt" href="altcat_3.html#E7:14_1_2"><i><font color="Green" title="E17">A7</font></i></a>, <a class="ref" href="altcat_3.html#D5" target="_self" title="ALTCAT_3:def.5">Def5</a></i>;<br/>


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