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<b>let </b><font color="Maroon" title="c1">A</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="altcat_1.html#V2" title="ALTCAT_1:attr.2">transitive</a>  <a href="altcat_1.html#L2" title="ALTCAT_1:struct.2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">B</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="altcat_1.html#V2" title="ALTCAT_1:attr.2">transitive</a>  <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c1">A</font>;<br/>



<a NAME="E1:62"/><i><font color="Green" title="E35">A1</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font> &amp; 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> &amp; the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</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#U2" title="ALTCAT_1:sel.2">Comp</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/>
<a NAME="E2:62"/><i><font color="Green" title="E36">A2</font></i>: 
( <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c1">A</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a>  <a href="yellow18.html#R2" title="YELLOW18:pred.2">are_opposite</a>  &amp; <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c2">B</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a>  <a href="yellow18.html#R2" title="YELLOW18:pred.2">are_opposite</a>  )
 
<b>by </b><i><a class="ref" href="yellow18.html#D4" title="YELLOW18:def.4">YELLOW18:def 4</a></i>;<br/>
<a NAME="E3:62"/><b>then </b><i><font color="Green" title="E37">A3</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font> )
 
<b>by </b><i><a class="ref" href="yellow18.html#D3" title="YELLOW18:def.3">YELLOW18:def 3</a></i>;<br/>
<b>hence </b><a NAME="E4:62"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span>
 <b>by </b><i><a class="ref" href="altcat_2.html#D11" title="ALTCAT_2:def.11">ALTCAT_2:def 11</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_2.html#D11" title="ALTCAT_2:def.11">ALTCAT_2:def 11</a><br/>

<a NAME="E5:62"/>
( the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="altcat_2.html#K1" title="ALTCAT_2:func.1">~</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font> &amp; the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="altcat_2.html#K1" title="ALTCAT_2:func.1">~</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font> )
 
<b>by </b><i><a class="txt" href="yellow20.html#E2:62"><i><font color="Green" title="E36">A2</font></i></a>, <a class="ref" href="yellow18.html#D3" title="YELLOW18:def.3">YELLOW18:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:62"/>
the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span> <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 <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span>
 <b>by </b><i><a class="txt" href="yellow20.html#E1:62"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="yellow20.html#T47" target="_self" title="YELLOW20:th.47">Th47</a></i>;<br/>

<b>thus </b><a NAME="E7:62"/>
<span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 <b>by </b><i><a class="txt" href="yellow20.html#E1:62"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="yellow20.html#E3:62"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="mcart_1.html#T77" title="MCART_1:th.77">MCART_1:77</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_2.html#D2" title="ALTCAT_2:def.2">ALTCAT_2:def 2</a><br/>

<b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E8:62"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">x1</font>, <font color="Maroon" title="c5">x2</font>, <font color="Maroon" title="c6">x3</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E10:62"/><i><font color="Green" title="E38">A4</font></i>: 
( <font color="Maroon" title="c4">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font> &amp; <font color="Maroon" title="c5">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font> &amp; <font color="Maroon" title="c6">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font> &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">x3</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> )
 <b>by </b><i><a class="txt" href="yellow20.html#E3:62"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="mcart_1.html#T72" title="MCART_1:th.72">MCART_1:72</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">a</font> = <font color="Maroon" title="c4">x1</font>, <font color="Maroon" title="c8">b</font> = <font color="Maroon" title="c5">x2</font>, <font color="Maroon" title="c9">c</font> = <font color="Maroon" title="c6">x3</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">B</font> <b>by </b><i><a class="txt" href="yellow20.html#E10:62"><i><font color="Green" title="E38">A4</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">a1</font> = <font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c11">b1</font> = <font color="Maroon" title="c8">b</font>, <font color="Maroon" title="c12">c1</font> = <font color="Maroon" title="c9">c</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font> <b>by </b><i><a class="txt" href="yellow20.html#E1:62"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="yellow20.html#E10:62"><i><font color="Green" title="E38">A4</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c13">a'</font> = <font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c14">b'</font> = <font color="Maroon" title="c8">b</font>, <font color="Maroon" title="c15">c'</font> = <font color="Maroon" title="c9">c</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span> <b>by </b><i><a class="txt" href="yellow20.html#E2:62"><i><font color="Green" title="E36">A2</font></i></a>, <a class="ref" href="yellow18.html#D3" title="YELLOW18:def.3">YELLOW18:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c16">a1'</font> = <font color="Maroon" title="c10">a1</font>, <font color="Maroon" title="c17">b1'</font> = <font color="Maroon" title="c11">b1</font>, <font color="Maroon" title="c18">c1'</font> = <font color="Maroon" title="c12">c1</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span> <b>by </b><i><a class="txt" href="yellow20.html#E2:62"><i><font color="Green" title="E36">A2</font></i></a>, <a class="ref" href="yellow18.html#D3" title="YELLOW18:def.3">YELLOW18:def 3</a></i>;<br/>
<a NAME="E15:62"/><i><font color="Green" title="E39">A5</font></i>: 
the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c14">b'</font>,<font color="Maroon" title="c15">c'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="functor0.html#K1" title="FUNCTOR0:func.1">~</a> <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="c2">B</font> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c7">a</font></span>)</span>
 
<b>by </b><i><a class="txt" href="yellow20.html#E2:62"><i><font color="Green" title="E36">A2</font></i></a>, <a class="ref" href="yellow18.html#D3" title="YELLOW18:def.3">YELLOW18:def 3</a></i>;<br/>
<a NAME="E16:62"/><i><font color="Green" title="E40">A6</font></i>: 
the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> <font color="Maroon" title="c16">a1'</font>,<font color="Maroon" title="c17">b1'</font>,<font color="Maroon" title="c18">c1'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="functor0.html#K1" title="FUNCTOR0:func.1">~</a> <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">A</font> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> <font color="Maroon" title="c12">c1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c10">a1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="yellow20.html#E2:62"><i><font color="Green" title="E36">A2</font></i></a>, <a class="ref" href="yellow18.html#D3" title="YELLOW18:def.3">YELLOW18:def 3</a></i>;<br/>
<a NAME="E17:62"/><i><font color="Green" title="E41">A7</font></i>: 
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c4">x1</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</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>,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#K3" title="ZFMISC_1:func.3">:]</a></span>
 
<b>by </b><i><a class="txt" href="yellow20.html#E10:62"><i><font color="Green" title="E38">A4</font></i></a>, <a class="ref" href="mcart_1.html#T73" title="MCART_1:th.73">MCART_1:73</a></i>;<br/>
<a NAME="E18:62"/><i><font color="Green" title="E42">A8</font></i>: 
( the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c14">b'</font>,<font color="Maroon" title="c15">c'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> &amp; the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> <font color="Maroon" title="c16">a1'</font>,<font color="Maroon" title="c17">b1'</font>,<font color="Maroon" title="c18">c1'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> )
 
<b>by </b><i><a class="txt" href="yellow20.html#E10:62"><i><font color="Green" title="E38">A4</font></i></a>, <a class="ref" href="multop_1.html#D1" title="MULTOP_1:def.1">MULTOP_1:def 1</a></i>;<br/>
<a NAME="E19:62"/>
( the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon" title="c2">B</font> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</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="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c7">a</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> &amp; the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon" title="c1">A</font> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> <font color="Maroon" title="c12">c1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c10">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</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="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c12">c1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c10">a1</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> )
 
<b>by </b><i><a class="ref" href="multop_1.html#D1" title="MULTOP_1:def.1">MULTOP_1:def 1</a></i>;<br/>
<a NAME="E20:62"/><b>then </b>
the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon" title="c2">B</font> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c7">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon" title="c1">A</font> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> <font color="Maroon" title="c12">c1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c10">a1</font>
 
<b>by </b><i><a class="txt" href="yellow20.html#E1:62"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="yellow20.html#E17:62"><i><font color="Green" title="E41">A7</font></i></a>, <a class="ref" href="altcat_2.html#D2" title="ALTCAT_2:def.2">ALTCAT_2:def 2</a></i>;<br/>
<b>hence </b><a NAME="E21:62"/>
the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font>
 <b>by </b><i><a class="txt" href="yellow20.html#E15:62"><i><font color="Green" title="E39">A5</font></i></a>, <a class="txt" href="yellow20.html#E16:62"><i><font color="Green" title="E40">A6</font></i></a>, <a class="txt" href="yellow20.html#E18:62"><i><font color="Green" title="E42">A8</font></i></a>, <a class="ref" href="yellow20.html#T45" target="_self" title="YELLOW20:th.45">Th45</a></i>;<br/>


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