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<span class="kw">let </span><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#V2" title="ALTCAT_1:attr.2">transitive</a>   <a href="altcat_1.html#L2" title="ALTCAT_1:struct.2">AltCatStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_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> holds  <font color="Olive" title="b1">B</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a>  is    <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c1">A</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span><br/><span class="kw">let </span><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_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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">B</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a>  is    <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c1">A</font> <a href="yellow18.html#K1" title="YELLOW18:func.1">opp</a> </span><br/>



<a NAME="E1:59"/><span class="lab"><font color="Green" title="E34">A1</font></span>: 
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow18.html#D4" title="YELLOW18:def.4">YELLOW18:def 4</a></span>;<br/>
<a NAME="E2:59"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A2</font></span>: 
 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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow18.html#D3" title="YELLOW18:def.3">YELLOW18:def 3</a></span>;<br/>
<a NAME="E3:59"/><span class="lab"><font color="Green" title="E36">A3</font></span>: 
 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="funct_4.html#K2" title="FUNCT_4:func.2">~</a>  the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="ref" href="yellow18.html#D3" title="YELLOW18:def.3">YELLOW18:def 3</a></span>;<br/>
<a NAME="E4:59"/><span class="lab"><font color="Green" title="E37">A4</font></span>: 
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow18.html#D4" title="YELLOW18:def.4">YELLOW18:def 4</a></span>;<br/>
<a NAME="E5:59"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A5</font></span>: 
 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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow18.html#D3" title="YELLOW18:def.3">YELLOW18:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:59"/>
 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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:59"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="ref" href="altcat_2.html#D11" title="ALTCAT_2:def.11">ALTCAT_2:def 11</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="altcat_2.html#D11" title="ALTCAT_2:def.11">ALTCAT_2:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  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> &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="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#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> )</span><br/>

<a NAME="E7:59"/>
(  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#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="funct_4.html#K2" title="FUNCT_4:func.2">~</a>  the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:59"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="ref" href="altcat_2.html#D11" title="ALTCAT_2:def.11">ALTCAT_2:def 11</a>, <a class="ref" href="yellow18.html#D3" title="YELLOW18:def.3">YELLOW18:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:59"/>
 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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:59"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="ref" href="yellow20.html#T46" target="_self" title="YELLOW20:th.46">Th47</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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_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 <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></span><br/>

<a NAME="E9:59"/><span class="lab"><font color="Green" title="E39">A6</font></span>: 
 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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_2.html#D11" title="ALTCAT_2:def.11">ALTCAT_2:def 11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:59"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:59"><span class="lab"><font color="Green" title="E38">A5</font></span></a>, <a class="txt" href="#E2:59"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="ref" href="mcart_1.html#T73" title="MCART_1:th.73">MCART_1:73</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="altcat_2.html#D2" title="ALTCAT_2:def.2">ALTCAT_2:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></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> or  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="Olive">b<sub>1</sub></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="Olive">b<sub>1</sub></font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <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> or  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> )</span><br/>

<span class="kw">assume </span><a NAME="E11:59"/>
<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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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></span><br/>

<span class="kw">then </span><span class="kw">consider </span><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> <span class="kw"> such that </span><br/><a NAME="E13:59"/><span class="lab"><font color="Green" title="E40">A7</font></span>: 
( <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> )
 <span class="kw">and </span><br/><a NAME="E14:59"/><span class="lab"><font color="Green" title="E41">A8</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:59"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>;<br/>
<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:59"><span class="lab"><font color="Green" title="E40">A7</font></span></a></span>;<br/>
<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:59"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E13:59"><span class="lab"><font color="Green" title="E40">A7</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">a19</font> = <font color="Maroon" title="c10">a1</font>, <font color="Maroon" title="c14">b19</font> = <font color="Maroon" title="c11">b1</font>, <font color="Maroon" title="c15">c19</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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:59"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="ref" href="yellow18.html#D3" title="YELLOW18:def.3">YELLOW18:def 3</a></span>;<br/>
<a NAME="E18:59"/><span class="lab"><font color="Green" title="E42">A9</font></span>: 
(  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> &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_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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_2.html#D11" title="ALTCAT_2:def.11">ALTCAT_2:def 11</a>, <a class="ref" href="multop_1.html#D1" title="MULTOP_1:def.1">MULTOP_1:def 1</a></span>;<br/>
<a NAME="E19:59"/><span class="lab"><font color="Green" title="E43">A10</font></span>: 
 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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="multop_1.html#D1" title="MULTOP_1:def.1">MULTOP_1:def 1</a></span>;<br/>
<a NAME="E20:59"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:59"><span class="lab"><font color="Green" title="E40">A7</font></span></a>, <a class="ref" href="mcart_1.html#T69" title="MCART_1:th.69">MCART_1:69</a></span>;<br/>
<a NAME="E21:59"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A11</font></span>: 
 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="relset_1.html#R1" title="RELSET_1: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>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:59"><span class="lab"><font color="Green" title="E42">A9</font></span></a>, <a class="txt" href="#E19:59"><span class="lab"><font color="Green" title="E43">A10</font></span></a>, <a class="ref" href="altcat_2.html#D2" title="ALTCAT_2:def.2">ALTCAT_2:def 2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c16">a9</font> = <font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c17">b9</font> = <font color="Maroon" title="c8">b</font>, <font color="Maroon" title="c18">c9</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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="ref" href="yellow18.html#D3" title="YELLOW18:def.3">YELLOW18:def 3</a></span>;<br/>
<a NAME="E23:59"/><span class="lab"><font color="Green" title="E45">A12</font></span>: 
(  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="c16">a9</font>,<font color="Maroon" title="c17">b9</font>,<font color="Maroon" title="c18">c9</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="c13">a19</font>,<font color="Maroon" title="c14">b19</font>,<font color="Maroon" title="c15">c19</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> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:59"><span class="lab"><font color="Green" title="E41">A8</font></span></a>, <a class="ref" href="multop_1.html#D1" title="MULTOP_1:def.1">MULTOP_1:def 1</a></span>;<br/>
<a NAME="E24:59"/><span class="lab"><font color="Green" title="E46">A13</font></span>: 
 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="c13">a19</font>,<font color="Maroon" title="c14">b19</font>,<font color="Maroon" title="c15">c19</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:59"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="ref" href="yellow18.html#D3" title="YELLOW18:def.3">YELLOW18:def 3</a></span>;<br/>
<a NAME="E25:59"/>
 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="c16">a9</font>,<font color="Maroon" title="c17">b9</font>,<font color="Maroon" title="c18">c9</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="ref" href="yellow18.html#D3" title="YELLOW18:def.3">YELLOW18:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E26:59"/>
 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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:59"><span class="lab"><font color="Green" title="E46">A13</font></span></a>, <a class="txt" href="#E23:59"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="txt" href="#E21:59"><span class="lab"><font color="Green" title="E44">A11</font></span></a>, <a class="ref" href="yellow20.html#T44" target="_self" title="YELLOW20:th.44">Th45</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
