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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> <a href="isocat_1.html#NR2" title="ISOCAT_1:NR.2">~=</a> <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">X</font> = <span class="p1">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p1">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">Y</font> = <span class="p1"><a href="cat_2.html#K19" title="CAT_2:func.19">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p3">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p4"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<span class="p3"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span><a href="cat_2.html#K19" title="CAT_2:func.19">:&gt;</a></span>;<br/>
<span class="kw">take </span><font color="Maroon" title="c6">F</font> = <span class="p1"><a href="cat_2.html#K19" title="CAT_2:func.19">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p3">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p4"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span>,<span class="p2"><a href="cat_2.html#K19" title="CAT_2:func.19">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<span class="p4"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span><a href="cat_2.html#K19" title="CAT_2:func.19">:&gt;</a></span></span><a href="cat_2.html#K19" title="CAT_2:func.19">:&gt;</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="isocat_1.html#D4" target="_self" title="ISOCAT_1:def.4">ISOCAT_1:def 4</a> <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="c6">F</font> is  <a href="cat_1.html#V8" title="CAT_1:attr.8">isomorphic</a> </span><br/>

<a NAME="E1:22"/><span class="lab"><font color="Green" title="E14">A1</font></span>: 
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p2">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p3"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E2:22"/><span class="lab"><font color="Green" title="E15">A2</font></span>: 
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p2">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p3"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="cat_2.html#K19" title="CAT_2:func.19">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p3">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p4"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<span class="p3"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span><a href="cat_2.html#K19" title="CAT_2:func.19">:&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">x</font>, <font color="Maroon" title="c8">y</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"> ( <font color="Maroon" title="c7">x</font> <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"><span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; <font color="Maroon" title="c8">y</font> <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"><span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; <font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y</font> implies <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font> )</span><br/><span class="kw">assume </span><a NAME="E1:22_1"/>
<font color="Maroon" title="c7">x</font> <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"><span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 ; <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="c8">y</font> <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"><span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; <font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y</font> implies <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font> )</span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">x1</font>, <font color="Maroon" title="c10">x2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:22_1"/><span class="lab"><font color="Green" title="E16">A3</font></span>: 
<font color="Maroon" title="c9">x1</font> <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#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">and </span><br/><a NAME="E4:22_1"/><span class="lab"><font color="Green" title="E17">A4</font></span>: 
<font color="Maroon" title="c10">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font>
 <span class="kw">and </span><br/><a NAME="E5:22_1"/><span class="lab"><font color="Green" title="E18">A5</font></span>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">x1</font>,<font color="Maroon" title="c10">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/><span class="kw">assume </span><a NAME="E6:22_1"/>
<font color="Maroon" title="c8">y</font> <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"><span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 ; <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="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y</font> implies <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font> )</span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">y1</font>, <font color="Maroon" title="c12">y2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E8:22_1"/><span class="lab"><font color="Green" title="E19">A6</font></span>: 
<font color="Maroon" title="c11">y1</font> <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#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">and </span><br/><a NAME="E9:22_1"/><span class="lab"><font color="Green" title="E20">A7</font></span>: 
<font color="Maroon" title="c12">y2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font>
 <span class="kw">and </span><br/><a NAME="E10:22_1"/><span class="lab"><font color="Green" title="E21">A8</font></span>: 
<font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">y1</font>,<font color="Maroon" title="c12">y2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c13">f2</font> = <font color="Maroon" title="c10">x2</font>, <font color="Maroon" title="c14">g2</font> = <font color="Maroon" title="c12">y2</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">C</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_1"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E9:22_1"><span class="lab"><font color="Green" title="E20">A7</font></span></a></span>;<br/><span class="kw">assume </span><a NAME="E12:22_1"/><span class="lab"><font color="Green" title="E22">A9</font></span>: 
<font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y</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="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font></span><br/><span class="kw">consider </span><font color="Maroon" title="c15">x11</font>, <font color="Maroon" title="c16">x12</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E14:22_1"/><span class="lab"><font color="Green" title="E23">A10</font></span>: 
<font color="Maroon" title="c15">x11</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font>
 <span class="kw">and </span><br/><a NAME="E15:22_1"/><span class="lab"><font color="Green" title="E24">A11</font></span>: 
<font color="Maroon" title="c16">x12</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font>
 <span class="kw">and </span><br/><a NAME="E16:22_1"/><span class="lab"><font color="Green" title="E25">A12</font></span>: 
<font color="Maroon" title="c9">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c15">x11</font>,<font color="Maroon" title="c16">x12</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_1"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c17">y11</font>, <font color="Maroon" title="c18">y12</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E18:22_1"/><span class="lab"><font color="Green" title="E26">A13</font></span>: 
<font color="Maroon" title="c17">y11</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font>
 <span class="kw">and </span><br/><a NAME="E19:22_1"/><span class="lab"><font color="Green" title="E27">A14</font></span>: 
<font color="Maroon" title="c18">y12</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font>
 <span class="kw">and </span><br/><a NAME="E20:22_1"/><span class="lab"><font color="Green" title="E28">A15</font></span>: 
<font color="Maroon" title="c11">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c17">y11</font>,<font color="Maroon" title="c18">y12</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:22_1"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c19">f12</font> = <font color="Maroon" title="c16">x12</font>, <font color="Maroon" title="c20">g12</font> = <font color="Maroon" title="c18">y12</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">B</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:22_1"><span class="lab"><font color="Green" title="E24">A11</font></span></a>, <a class="txt" href="#E19:22_1"><span class="lab"><font color="Green" title="E27">A14</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c21">f11</font> = <font color="Maroon" title="c15">x11</font>, <font color="Maroon" title="c22">g11</font> = <font color="Maroon" title="c17">y11</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">A</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:22_1"><span class="lab"><font color="Green" title="E23">A10</font></span></a>, <a class="txt" href="#E18:22_1"><span class="lab"><font color="Green" title="E26">A13</font></span></a></span>;<br/><span class="lab"><font color="Green" title="E29">A16</font></span>: <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c21">f11</font>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c19">f12</font>,<font color="Maroon" title="c13">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> = 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<font color="Maroon" title="c21">f11</font>,<font color="Maroon" title="c19">f12</font>)</span>)</span>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c19">f12</font>,<font color="Maroon" title="c13">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D4" title="FUNCT_3:def.4">FUNCT_3:def 4</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c21">f11</font>,<font color="Maroon" title="c19">f12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">f2</font>)</span>)</span></span>)</span>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c19">f12</font>,<font color="Maroon" title="c13">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D4" title="FUNCT_3:def.4">FUNCT_3:def 4</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p5"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c21">f11</font>,<font color="Maroon" title="c19">f12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span></span>)</span>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c19">f12</font>,<font color="Maroon" title="c13">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>

<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c21">f11</font>,<font color="Maroon" title="c19">f12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">f2</font>)</span>)</span>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c19">f12</font>,<font color="Maroon" title="c13">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T15" title="FUNCT_2:th.15">FUNCT_2:15</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c21">f11</font>,<font color="Maroon" title="c19">f12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<font color="Maroon" title="c21">f11</font>,<font color="Maroon" title="c19">f12</font>)</span>)</span>,<font color="Maroon" title="c13">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D5" title="FUNCT_3:def.5">FUNCT_3:def 5</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c21">f11</font>,<font color="Maroon" title="c19">f12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p0"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<span class="p5"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c21">f11</font>,<font color="Maroon" title="c19">f12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">f2</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c13">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D4" title="FUNCT_3:def.4">FUNCT_3:def 4</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c21">f11</font>,<font color="Maroon" title="c19">f12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p5">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p0"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p5"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c21">f11</font>,<font color="Maroon" title="c19">f12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>,<font color="Maroon" title="c13">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T15" title="FUNCT_2:th.15">FUNCT_2:15</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c21">f11</font>,<font color="Maroon" title="c19">f12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p5">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p0"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p5"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c21">f11</font>,<font color="Maroon" title="c19">f12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c21">f11</font>,<font color="Maroon" title="c19">f12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">f2</font>)</span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D5" title="FUNCT_3:def.5">FUNCT_3:def 5</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c21">f11</font>,<font color="Maroon" title="c19">f12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="cat_2.html#K19" title="CAT_2:func.19">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p5">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p0"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span><a href="cat_2.html#K19" title="CAT_2:func.19">:&gt;</a></span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c21">f11</font>,<font color="Maroon" title="c19">f12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="funct_3.html#T49" title="FUNCT_3:th.49">FUNCT_3:49</a></span>
<br/>.= 
<font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c22">g11</font>,<font color="Maroon" title="c20">g12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E5:22_1"><span class="lab"><font color="Green" title="E18">A5</font></span></a>, <a class="txt" href="#E16:22_1"><span class="lab"><font color="Green" title="E25">A12</font></span></a>, <a class="txt" href="#E10:22_1"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="txt" href="#E20:22_1"><span class="lab"><font color="Green" title="E28">A15</font></span></a>, <a class="txt" href="#E12:22_1"><span class="lab"><font color="Green" title="E22">A9</font></span></a>, <a class="ref" href="funct_3.html#T49" title="FUNCT_3:th.49">FUNCT_3:49</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c22">g11</font>,<font color="Maroon" title="c20">g12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="cat_2.html#K19" title="CAT_2:func.19">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p5">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p0"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span><a href="cat_2.html#K19" title="CAT_2:func.19">:&gt;</a></span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c22">g11</font>,<font color="Maroon" title="c20">g12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="ref" href="funct_3.html#T49" title="FUNCT_3:th.49">FUNCT_3:49</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c22">g11</font>,<font color="Maroon" title="c20">g12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p5">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p0"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p5"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c22">g11</font>,<font color="Maroon" title="c20">g12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c22">g11</font>,<font color="Maroon" title="c20">g12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c14">g2</font>)</span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="funct_3.html#T49" title="FUNCT_3:th.49">FUNCT_3:49</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c22">g11</font>,<font color="Maroon" title="c20">g12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p5">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p0"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p5"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c22">g11</font>,<font color="Maroon" title="c20">g12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D5" title="FUNCT_3:def.5">FUNCT_3:def 5</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c22">g11</font>,<font color="Maroon" title="c20">g12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p0"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<span class="p5"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c22">g11</font>,<font color="Maroon" title="c20">g12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c14">g2</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T15" title="FUNCT_2:th.15">FUNCT_2:15</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c22">g11</font>,<font color="Maroon" title="c20">g12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<font color="Maroon" title="c22">g11</font>,<font color="Maroon" title="c20">g12</font>)</span>)</span>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D4" title="FUNCT_3:def.4">FUNCT_3:def 4</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c22">g11</font>,<font color="Maroon" title="c20">g12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c20">g12</font>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D5" title="FUNCT_3:def.5">FUNCT_3:def 5</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c22">g11</font>,<font color="Maroon" title="c20">g12</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c14">g2</font>)</span>)</span></span>)</span>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c20">g12</font>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T15" title="FUNCT_2:th.15">FUNCT_2:15</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<font color="Maroon" title="c22">g11</font>,<font color="Maroon" title="c20">g12</font>)</span>)</span>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c20">g12</font>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D4" title="FUNCT_3:def.4">FUNCT_3:def 4</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c22">g11</font>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c20">g12</font>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D4" title="FUNCT_3:def.4">FUNCT_3:def 4</a></span>
;<br/><a NAME="E24:22_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">x12</font>,<font color="Maroon" title="c10">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c18">y12</font>,<font color="Maroon" title="c12">y2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</a></span>;<br/><a NAME="E25:22_1"/><span class="kw">then </span>
( <font color="Maroon" title="c16">x12</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">y12</font> &amp; <font color="Maroon" title="c10">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">y2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</a></span>;<br/><span class="kw">hence </span><a NAME="E26:22_1"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:22_1"><span class="lab"><font color="Green" title="E18">A5</font></span></a>, <a class="txt" href="#E16:22_1"><span class="lab"><font color="Green" title="E25">A12</font></span></a>, <a class="txt" href="#E10:22_1"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="txt" href="#E20:22_1"><span class="lab"><font color="Green" title="E28">A15</font></span></a>, <a class="txt" href="#E23:22_1"><span class="lab"><font color="Green" title="E29">A16</font></span></a>, <a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:22"/>
<font color="Maroon" title="c6">F</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T19" title="FUNCT_2:th.19">FUNCT_2:19</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="isocat_1.html#D3" target="_self" title="ISOCAT_1:def.3">ISOCAT_1:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c6">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span><br/>

<span class="kw">thus </span><a NAME="E5:22"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c6">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</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="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c6">F</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c7">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</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="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> or <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c6">F</font> )</span><br/>

<span class="kw">assume </span><a NAME="E6:22"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>
 ; <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="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c6">F</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">x1</font>, <font color="Maroon" title="c9">x2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E8:22"/><span class="lab"><font color="Green" title="E16">A17</font></span>: 
<font color="Maroon" title="c8">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font>
 <span class="kw">and </span><br/><a NAME="E9:22"/><span class="lab"><font color="Green" title="E17">A18</font></span>: 
<font color="Maroon" title="c9">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>
 <span class="kw">and </span><br/><a NAME="E10:22"/><span class="lab"><font color="Green" title="E18">A19</font></span>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">x1</font>,<font color="Maroon" title="c9">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">x1</font> = <font color="Maroon" title="c8">x1</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">A</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:22"><span class="lab"><font color="Green" title="E16">A17</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c11">x21</font>, <font color="Maroon" title="c12">x22</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E13:22"/><span class="lab"><font color="Green" title="E19">A20</font></span>: 
<font color="Maroon" title="c11">x21</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font>
 <span class="kw">and </span><br/><a NAME="E14:22"/><span class="lab"><font color="Green" title="E20">A21</font></span>: 
<font color="Maroon" title="c12">x22</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font>
 <span class="kw">and </span><br/><a NAME="E15:22"/><span class="lab"><font color="Green" title="E21">A22</font></span>: 
<font color="Maroon" title="c9">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">x21</font>,<font color="Maroon" title="c12">x22</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:22"><span class="lab"><font color="Green" title="E17">A18</font></span></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">x22</font> = <font color="Maroon" title="c12">x22</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">C</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:22"><span class="lab"><font color="Green" title="E20">A21</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">x21</font> = <font color="Maroon" title="c11">x21</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">B</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:22"><span class="lab"><font color="Green" title="E19">A20</font></span></a></span>;<br/>
<font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<font color="Maroon" title="c14">x21</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">x22</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> = 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<font color="Maroon" title="c14">x21</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">x22</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="cat_2.html#K19" title="CAT_2:func.19">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p5">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p0"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span><a href="cat_2.html#K19" title="CAT_2:func.19">:&gt;</a></span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<font color="Maroon" title="c14">x21</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">x22</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="ref" href="funct_3.html#T49" title="FUNCT_3:th.49">FUNCT_3:49</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<font color="Maroon" title="c14">x21</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">x22</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="cat_2.html#K19" title="CAT_2:func.19">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p5">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p0"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span><a href="cat_2.html#K19" title="CAT_2:func.19">:&gt;</a></span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<font color="Maroon" title="c14">x21</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">x22</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T15" title="FUNCT_2:th.15">FUNCT_2:15</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<font color="Maroon" title="c10">x1</font>,<font color="Maroon" title="c14">x21</font>)</span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="cat_2.html#K19" title="CAT_2:func.19">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p5">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p0"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span><a href="cat_2.html#K19" title="CAT_2:func.19">:&gt;</a></span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<font color="Maroon" title="c14">x21</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">x22</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D4" title="FUNCT_3:def.4">FUNCT_3:def 4</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<span class="p2">(<span class="default"><span class="p3"><a href="cat_2.html#K19" title="CAT_2:func.19">&lt;:</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p5">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p0"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span><a href="cat_2.html#K19" title="CAT_2:func.19">:&gt;</a></span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<font color="Maroon" title="c14">x21</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">x22</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D4" title="FUNCT_3:def.4">FUNCT_3:def 4</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p5">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p0"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p5"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<font color="Maroon" title="c14">x21</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">x22</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p5"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<font color="Maroon" title="c14">x21</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">x22</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="funct_3.html#T49" title="FUNCT_3:th.49">FUNCT_3:49</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> (<span class="p0"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<span class="p5"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<font color="Maroon" title="c14">x21</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">x22</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p5"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<font color="Maroon" title="c14">x21</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">x22</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T15" title="FUNCT_2:th.15">FUNCT_2:15</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>)</span>)</span> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<font color="Maroon" title="c10">x1</font>,<font color="Maroon" title="c14">x21</font>)</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<font color="Maroon" title="c14">x21</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">x22</font>)</span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D4" title="FUNCT_3:def.4">FUNCT_3:def 4</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c14">x21</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> (<span class="p5"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>)</span>)</span> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<span class="p4"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<font color="Maroon" title="c14">x21</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c13">x22</font>)</span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D5" title="FUNCT_3:def.5">FUNCT_3:def 5</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c10">x1</font>,<span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c14">x21</font>,<font color="Maroon" title="c13">x22</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D5" title="FUNCT_3:def.5">FUNCT_3:def 5</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E19:22"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c6">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:22"><span class="lab"><font color="Green" title="E18">A19</font></span></a>, <a class="txt" href="#E15:22"><span class="lab"><font color="Green" title="E21">A22</font></span></a>, <a class="ref" href="funct_2.html#T4" title="FUNCT_2:th.4">FUNCT_2:4</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>
