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<b>let </b><font color="Maroon" title="c1">A</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <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"> for <font color="Olive" title="b1">B</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b2">o1</font>, <font color="Olive" title="b3">o2</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Olive" title="b1">B</font> holds  <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b2">o1</font>,<font color="Olive" title="b3">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Olive" title="b1">B</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b2">o1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Olive" title="b1">B</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b3">o2</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span></span><br/><b>let </b><font color="Maroon" title="c2">B</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</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">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="c2">B</font> holds  <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="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b1">o1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b2">o2</font></span>)</span></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">o1</font>, <font color="Maroon" title="c4">o2</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"> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c4">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c3">o1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c4">o2</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span></span><br/>





<a NAME="E1:76"/><i><font color="Green" title="E53">A1</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c4">o2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<i><font color="Green" title="E54">A2</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="c3">o1</font>,<font color="Maroon" title="c4">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> = 
the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c4">o2</font>
<b>by </b><i><a class="ref" href="altcat_1.html#D2" title="ALTCAT_1:def.2">ALTCAT_1:def 2</a></i>
<br/>.= 
the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c4">o2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>

;<br/>
<a NAME="E3:76"/><i><font color="Green" title="E55">A3</font></i>: 
<span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c3">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">o1</font>
 
<b>by </b><i><a class="ref" href="functor0.html#T28" target="_self" title="FUNCTOR0:th.28">Th28</a></i>;<br/>
<a NAME="E4:76"/>
<span class="p1">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c4">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">o2</font>
 
<b>by </b><i><a class="ref" href="functor0.html#T28" target="_self" title="FUNCTOR0:th.28">Th28</a></i>;<br/>
<b>then </b><i><font color="Green" title="E56">A4</font></i>: <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c3">o1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c4">o2</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> = 
the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c4">o2</font>
<b>by </b><i><a class="txt" href="functor0.html#E3:76"><i><font color="Green" title="E55">A3</font></i></a>, <a class="ref" href="altcat_1.html#D2" title="ALTCAT_1:def.2">ALTCAT_1:def 2</a></i>
<br/>.= 
the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c4">o2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>

;<br/>
<a NAME="E6:76"/>
the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="altcat_2.html#D11" title="ALTCAT_2:def.11">ALTCAT_2:def 11</a></i>;<br/>
<b>hence </b><a NAME="E7:76"/>
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c4">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c3">o1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c4">o2</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <b>by </b><i><a class="txt" href="functor0.html#E1:76"><i><font color="Green" title="E53">A1</font></i></a>, <a class="txt" href="functor0.html#E2:76"><i><font color="Green" title="E54">A2</font></i></a>, <a class="txt" href="functor0.html#E5:76"><i><font color="Green" title="E56">A4</font></i></a>, <a class="ref" href="altcat_2.html#D2" title="ALTCAT_2:def.2">ALTCAT_2:def 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/>


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