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<b>reconsider </b><font color="Maroon" title="c7">H1</font> = <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>, <font color="Maroon" title="c8">H2</font> = <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> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  <b>by </b><i><a class="txt" href="altcat_1.html#E1:28"><i><font color="Green" title="E15">A1</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">F</font> = the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon" title="c1">C</font> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> <font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c4">o3</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c8">H2</font>,<font color="Maroon" title="c7">H1</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<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> ;<br/>
<b>reconsider </b><font color="Maroon" title="c10">y</font> = <font color="Maroon" title="c6">g</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c8">H2</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c11">x</font> = <font color="Maroon" title="c5">f</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c7">H1</font> ;<br/>
<a NAME="E5:28_1_1"/>
<font color="Maroon" title="c9">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c10">y</font>,<font color="Maroon" title="c11">x</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <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>
 
;<br/>
<b>hence </b><a NAME="E6:28_1_1"/>
<span class="p1">(<span class="default">the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon" title="c1">C</font> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> <font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c4">o3</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c5">f</font> is   <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>
 ; <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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