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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be    <a href="altcat_1.html#L2" title="ALTCAT_1:struct.2">AltCatStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> <a href="yellow20.html#R1" title="YELLOW20:pred.1">have_the_same_composition</a>  implies for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b3">b1</font>, <font color="Olive" title="b4">b2</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">B</font><br/> for <font color="Olive" title="b5">o1</font>, <font color="Olive" title="b6">o2</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" title="YELLOW20:func.2">Intersect</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span>)</span>  st <font color="Olive" title="b5">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a1</font> &amp; <font color="Olive" title="b5">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">b1</font> &amp; <font color="Olive" title="b6">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a2</font> &amp; <font color="Olive" title="b6">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b2</font> &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b1">a1</font>,<font color="Olive" title="b2">a2</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="b3">b1</font>,<font color="Olive" title="b4">b2</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>  holds <br/>for <font color="Olive" title="b7">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b2">a2</font><br/> for <font color="Olive" title="b8">g</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">b2</font>  st <font color="Olive" title="b7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">g</font> holds <br/><font color="Olive" title="b7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b5">o1</font>,<font color="Olive" title="b6">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> )</span><br/>

<b>assume </b><a NAME="E1:27"/><i><font color="Green" title="E21">A1</font></i>: 
<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> <a href="yellow20.html#R1" title="YELLOW20:pred.1">have_the_same_composition</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">a1</font>, <font color="Olive" title="b2">a2</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b3">b1</font>, <font color="Olive" title="b4">b2</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">B</font><br/> for <font color="Olive" title="b5">o1</font>, <font color="Olive" title="b6">o2</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" title="YELLOW20:func.2">Intersect</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span>)</span>  st <font color="Olive" title="b5">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a1</font> &amp; <font color="Olive" title="b5">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">b1</font> &amp; <font color="Olive" title="b6">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a2</font> &amp; <font color="Olive" title="b6">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b2</font> &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b1">a1</font>,<font color="Olive" title="b2">a2</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="b3">b1</font>,<font color="Olive" title="b4">b2</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>  holds <br/>for <font color="Olive" title="b7">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b2">a2</font><br/> for <font color="Olive" title="b8">g</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">b2</font>  st <font color="Olive" title="b7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">g</font> holds <br/><font color="Olive" title="b7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b5">o1</font>,<font color="Olive" title="b6">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span></span><br/>

<b>let </b><font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c4">a2</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</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">b1</font>, <font color="Olive" title="b2">b2</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">B</font><br/> for <font color="Olive" title="b3">o1</font>, <font color="Olive" title="b4">o2</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" title="YELLOW20:func.2">Intersect</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span>)</span>  st <font color="Olive" title="b3">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a1</font> &amp; <font color="Olive" title="b3">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b1</font> &amp; <font color="Olive" title="b4">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a2</font> &amp; <font color="Olive" title="b4">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b2</font> &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">a1</font>,<font color="Maroon" title="c4">a2</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="b1">b1</font>,<font color="Olive" title="b2">b2</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>  holds <br/>for <font color="Olive" title="b5">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font><br/> for <font color="Olive" title="b6">g</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">b1</font>,<font color="Olive" title="b2">b2</font>  st <font color="Olive" title="b5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">g</font> holds <br/><font color="Olive" title="b5">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b3">o1</font>,<font color="Olive" title="b4">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span></span><br/><b>let </b><font color="Maroon" title="c5">b1</font>, <font color="Maroon" title="c6">b2</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">B</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">o1</font>, <font color="Olive" title="b2">o2</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" title="YELLOW20:func.2">Intersect</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span>)</span>  st <font color="Olive" title="b1">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a1</font> &amp; <font color="Olive" title="b1">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b1</font> &amp; <font color="Olive" title="b2">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a2</font> &amp; <font color="Olive" title="b2">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b2</font> &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">a1</font>,<font color="Maroon" title="c4">a2</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">b1</font>,<font color="Maroon" title="c6">b2</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>  holds <br/>for <font color="Olive" title="b3">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font><br/> for <font color="Olive" title="b4">g</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</font>  st <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">g</font> holds <br/><font color="Olive" title="b3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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></span><br/><b>let </b><font color="Maroon" title="c7">o1</font>, <font color="Maroon" title="c8">o2</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" title="YELLOW20:func.2">Intersect</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a1</font> &amp; <font color="Maroon" title="c7">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b1</font> &amp; <font color="Maroon" title="c8">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c8">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b2</font> &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">a1</font>,<font color="Maroon" title="c4">a2</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">b1</font>,<font color="Maroon" title="c6">b2</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>  implies for <font color="Olive" title="b1">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font><br/> for <font color="Olive" title="b2">g</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</font>  st <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g</font> holds <br/><font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> )</span><br/>





<b>assume </b><a NAME="E2:27"/>
( <font color="Maroon" title="c7">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a1</font> &amp; <font color="Maroon" title="c7">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b1</font> &amp; <font color="Maroon" title="c8">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c8">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</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>  or  not <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</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>  or for <font color="Olive" title="b1">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font><br/> for <font color="Olive" title="b2">g</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</font>  st <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g</font> holds <br/><font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> )</span><br/>

<a NAME="E3:27"/><b>then </b>
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 
<b>by </b><i><a class="txt" href="#E1:27"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="yellow20.html#T22" target="_self" title="YELLOW20:th.22">Th22</a></i>;<br/>
<b>hence </b><a NAME="E4:27"/>
(  not <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</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>  or  not <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</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>  or for <font color="Olive" title="b1">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font><br/> for <font color="Olive" title="b2">g</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</font>  st <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g</font> holds <br/><font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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