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<span class="kw">let </span><font color="Maroon" title="c1">C1</font>, <font color="Maroon" title="c2">C2</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">  for <font color="Olive" title="b1">F</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C1</font><br/>  for <font color="Olive" title="b5">f</font>, <font color="Olive" title="b6">g</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C1</font>  st <font color="Olive" title="b5">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>) &amp; <font color="Olive" title="b6">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font>) holds <br/> for <font color="Olive" title="b7">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>)  st <font color="Olive" title="b7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b6">g</font>,<font color="Olive" title="b5">f</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> holds <br/> for <font color="Olive" title="b8">H</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c2">C2</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> (<span class="p2">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K11" title="CATALG_1:func.11">Upsilon</a> <font color="Olive" title="b1">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K12" title="CATALG_1:func.12">Psi</a> <font color="Olive" title="b1">F</font></span>)</span>)</span>)</span>  st <font color="Olive" title="b8">H</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b1">F</font> <a href="catalg_1.html#K1" title="CATALG_1:func.1">-MSF</a> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>, the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>) holds <br/><font color="Olive" title="b8">H</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive" title="b7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">f</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">F</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C1</font><br/>  for <font color="Olive" title="b4">f</font>, <font color="Olive" title="b5">g</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C1</font>  st <font color="Olive" title="b4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) &amp; <font color="Olive" title="b5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>) holds <br/> for <font color="Olive" title="b6">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>)  st <font color="Olive" title="b6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b5">g</font>,<font color="Olive" title="b4">f</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> holds <br/> for <font color="Olive" title="b7">H</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c2">C2</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> (<span class="p2">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K11" title="CATALG_1:func.11">Upsilon</a> <font color="Maroon" title="c3">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K12" title="CATALG_1:func.12">Psi</a> <font color="Maroon" title="c3">F</font></span>)</span>)</span>)</span>  st <font color="Olive" title="b7">H</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">F</font> <a href="catalg_1.html#K1" title="CATALG_1:func.1">-MSF</a> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>, the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>) holds <br/><font color="Olive" title="b7">H</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive" title="b6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">f</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><br/>



<span class="kw">set </span><font color="Maroon" title="c4">CS1</font> =  <a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">CS2</font> =  <a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">A1</font> =  <a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">A2</font> =  <a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c2">C2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">u</font> =  <a href="catalg_1.html#K11" title="CATALG_1:func.11">Upsilon</a> <font color="Maroon" title="c3">F</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">p</font> =  <a href="catalg_1.html#K12" title="CATALG_1:func.12">Psi</a> <font color="Maroon" title="c3">F</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">B</font> = <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c2">C2</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> (<span class="p1">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K11" title="CATALG_1:func.11">Upsilon</a> <font color="Maroon" title="c3">F</font></span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K12" title="CATALG_1:func.12">Psi</a> <font color="Maroon" title="c3">F</font></span>)</span>);<br/>
<span class="kw">let </span><font color="Maroon" title="c11">a</font>, <font color="Maroon" title="c12">b</font>, <font color="Maroon" title="c13">c</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C1</font>  st <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>) &amp; <font color="Olive" title="b2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>) holds <br/> for <font color="Olive" title="b3">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>)  st <font color="Olive" title="b3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b2">g</font>,<font color="Olive" title="b1">f</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> holds <br/> for <font color="Olive" title="b4">H</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c2">C2</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> (<span class="p2">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K11" title="CATALG_1:func.11">Upsilon</a> <font color="Maroon" title="c3">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K12" title="CATALG_1:func.12">Psi</a> <font color="Maroon" title="c3">F</font></span>)</span>)</span>)</span>  st <font color="Olive" title="b4">H</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">F</font> <a href="catalg_1.html#K1" title="CATALG_1:func.1">-MSF</a> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>, the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>) holds <br/><font color="Olive" title="b4">H</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive" title="b3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c14">o</font> =  <a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>);<br/>
<span class="kw">let </span><font color="Maroon" title="c15">f</font>, <font color="Maroon" title="c16">g</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C1</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="c15">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>) &amp; <font color="Maroon" title="c16">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>) implies  for <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>)  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c16">g</font>,<font color="Maroon" title="c15">f</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> holds <br/> for <font color="Olive" title="b2">H</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c2">C2</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> (<span class="p2">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K11" title="CATALG_1:func.11">Upsilon</a> <font color="Maroon" title="c3">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K12" title="CATALG_1:func.12">Psi</a> <font color="Maroon" title="c3">F</font></span>)</span>)</span>)</span>  st <font color="Olive" title="b2">H</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">F</font> <a href="catalg_1.html#K1" title="CATALG_1:func.1">-MSF</a> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>, the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>) holds <br/><font color="Olive" title="b2">H</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">f</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:65"/><span class="lab"><font color="Green" title="E34">A1</font></span>: 
<font color="Maroon" title="c15">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>)
 <span class="kw">and </span><br/><a NAME="E2:65"/><span class="lab"><font color="Green" title="E35">A2</font></span>: 
<font color="Maroon" title="c16">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>)  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c16">g</font>,<font color="Maroon" title="c15">f</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> holds <br/> for <font color="Olive" title="b2">H</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c2">C2</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> (<span class="p2">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K11" title="CATALG_1:func.11">Upsilon</a> <font color="Maroon" title="c3">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K12" title="CATALG_1:func.12">Psi</a> <font color="Maroon" title="c3">F</font></span>)</span>)</span>)</span>  st <font color="Olive" title="b2">H</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">F</font> <a href="catalg_1.html#K1" title="CATALG_1:func.1">-MSF</a> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>, the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>) holds <br/><font color="Olive" title="b2">H</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">f</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c17">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</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="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c16">g</font>,<font color="Maroon" title="c15">f</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> implies  for <font color="Olive" title="b1">H</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c2">C2</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> (<span class="p2">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K11" title="CATALG_1:func.11">Upsilon</a> <font color="Maroon" title="c3">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K12" title="CATALG_1:func.12">Psi</a> <font color="Maroon" title="c3">F</font></span>)</span>)</span>)</span>  st <font color="Olive" title="b1">H</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">F</font> <a href="catalg_1.html#K1" title="CATALG_1:func.1">-MSF</a> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>, the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>) holds <br/><font color="Olive" title="b1">H</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">f</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> )</span><br/>

<span class="kw">assume </span><a NAME="E3:65"/><span class="lab"><font color="Green" title="E36">A3</font></span>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c16">g</font>,<font color="Maroon" title="c15">f</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">H</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c2">C2</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> (<span class="p2">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K11" title="CATALG_1:func.11">Upsilon</a> <font color="Maroon" title="c3">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K12" title="CATALG_1:func.12">Psi</a> <font color="Maroon" title="c3">F</font></span>)</span>)</span>)</span>  st <font color="Olive" title="b1">H</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">F</font> <a href="catalg_1.html#K1" title="CATALG_1:func.1">-MSF</a> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>, the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>) holds <br/><font color="Olive" title="b1">H</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">f</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><br/>

<a NAME="E4:65"/>
<font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c13">c</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="ref" href="cat_1.html#T81" title="CAT_1:th.81">CAT_1:81</a></span>;<br/>
<a NAME="E5:65"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A4</font></span>: 
(  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c13">c</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T1" title="CAT_1:th.1">CAT_1:1</a></span>;<br/>
<a NAME="E6:65"/>
<font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="ref" href="cat_1.html#T81" title="CAT_1:th.81">CAT_1:81</a></span>;<br/>
<a NAME="E7:65"/><span class="kw">then </span>
(  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T1" title="CAT_1:th.1">CAT_1:1</a></span>;<br/>
<a NAME="E8:65"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A5</font></span>: 
<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">f</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c13">c</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c2">C2</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:65"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="ref" href="catalg_1.html#T28" target="_self" title="CATALG_1:th.28">Th39</a></span>;<br/>
<a NAME="E9:65"/><span class="lab"><font color="Green" title="E39">A6</font></span>: 
(  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c16">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b</font> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c16">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="ref" href="cat_1.html#T1" title="CAT_1:th.1">CAT_1:1</a></span>;<br/>
<a NAME="E10:65"/>
(  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c15">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a</font> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c15">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="ref" href="cat_1.html#T1" title="CAT_1:th.1">CAT_1:1</a></span>;<br/>
<a NAME="E11:65"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A7</font></span>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:65"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="txt" href="#E9:65"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="ref" href="catalg_1.html#T28" target="_self" title="CATALG_1:th.28">Th39</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c18">H</font> be   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c2">C2</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> (<span class="p2">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K11" title="CATALG_1:func.11">Upsilon</a> <font color="Maroon" title="c3">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K12" title="CATALG_1:func.12">Psi</a> <font color="Maroon" title="c3">F</font></span>)</span>)</span>)</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="c18">H</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">F</font> <a href="catalg_1.html#K1" title="CATALG_1:func.1">-MSF</a> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>, the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span>) implies <font color="Maroon" title="c18">H</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">f</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> )</span><br/>

<span class="kw">assume </span><a NAME="E12:65"/><span class="lab"><font color="Green" title="E41">A8</font></span>: 
<font color="Maroon" title="c18">H</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">F</font> <a href="catalg_1.html#K1" title="CATALG_1:func.1">-MSF</a> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>, the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</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="c18">H</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">f</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><br/>

<a NAME="E13:65"/>
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> (<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="catalg_1.html#D13" target="_self" title="CATALG_1:def.13">Def15</a></span>;<br/>
<a NAME="E14:65"/><span class="kw">then </span>
<font color="Maroon" title="c18">H</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> (<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:65"><span class="lab"><font color="Green" title="E41">A8</font></span></a>, <a class="ref" href="catalg_1.html#D1" target="_self" title="CATALG_1:def.1">Def1</a></span>;<br/>
<a NAME="E15:65"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A9</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c18">H</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p2">(<span class="default"><a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> (<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="ref" href="funct_1.html#T49" title="FUNCT_1:th.49">FUNCT_1:49</a></span>;<br/>
<a NAME="E16:65"/><span class="lab"><font color="Green" title="E43">A10</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c16">g</font>,<font color="Maroon" title="c15">f</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T89" title="FINSEQ_1:th.89">FINSEQ_1:89</a></span>;<br/>
<a NAME="E17:65"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A11</font></span>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c16">g</font>,<font color="Maroon" title="c15">f</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T2" title="FINSEQ_1:th.2">FINSEQ_1:2</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<a NAME="E18:65"/>
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="catalg_1.html#D13" target="_self" title="CATALG_1:def.13">Def15</a></span>;<br/>
<a NAME="E19:65"/><span class="kw">then </span>
<font color="Maroon" title="c18">H</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:65"><span class="lab"><font color="Green" title="E41">A8</font></span></a>, <a class="ref" href="catalg_1.html#D1" target="_self" title="CATALG_1:def.1">Def1</a></span>;<br/>
<a NAME="E20:65"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A12</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c18">H</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p2">(<span class="default"><a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="ref" href="funct_1.html#T49" title="FUNCT_1:th.49">FUNCT_1:49</a></span>;<br/>
<a NAME="E21:65"/><span class="lab"><font color="Green" title="E46">A13</font></span>: 
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c16">g</font>,<font color="Maroon" title="c15">f</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:65"><span class="lab"><font color="Green" title="E43">A10</font></span></a>, <a class="ref" href="finseq_1.html#T2" title="FINSEQ_1:th.2">FINSEQ_1:2</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<a NAME="E22:65"/>
 <a href="catalg_1.html#K11" title="CATALG_1:func.11">Upsilon</a> <font color="Maroon" title="c3">F</font>, <a href="catalg_1.html#K12" title="CATALG_1:func.12">Psi</a> <font color="Maroon" title="c3">F</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a>  <a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font>, <a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="catalg_1.html#T23" target="_self" title="CATALG_1:th.23">Th33</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E47">A14</font></span>:  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>)</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c2">C2</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> (<span class="p2">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K11" title="CATALG_1:func.11">Upsilon</a> <font color="Maroon" title="c3">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K12" title="CATALG_1:func.12">Psi</a> <font color="Maroon" title="c3">F</font></span>)</span>)</span>)</span>) = 
 <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K12" title="CATALG_1:func.12">Psi</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c2">C2</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="instalg1.html#T24" title="INSTALG1:th.24">INSTALG1:24</a></span>
<br/>.= 
 <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c13">c</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c2">C2</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="catalg_1.html#T22" target="_self" title="CATALG_1:th.22">Th32</a></span>
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c19">g9</font>, <font color="Maroon" title="c20">f9</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">C2</font><span class="kw"> such that </span><br/><a NAME="E25:65"/><span class="lab"><font color="Green" title="E48">A15</font></span>: 
<font color="Maroon" title="c18">H</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c19">g9</font>,<font color="Maroon" title="c20">f9</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 <span class="kw">and </span><br/><a NAME="E26:65"/>
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c20">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">a</font>
 <span class="kw">and </span><br/><a NAME="E27:65"/>
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c20">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font>
 <span class="kw">and </span><br/><a NAME="E28:65"/>
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c19">g9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">b</font>
 <span class="kw">and </span><br/><a NAME="E29:65"/>
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c19">g9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c13">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:65"><span class="lab"><font color="Green" title="E38">A5</font></span></a>, <a class="ref" href="catalg_1.html#T28" target="_self" title="CATALG_1:th.28">Th39</a></span>;<br/>
<a NAME="E30:65"/><span class="lab"><font color="Green" title="E49">A16</font></span>: 
<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c19">g9</font>,<font color="Maroon" title="c20">f9</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">g9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/>
<a NAME="E31:65"/><span class="lab"><font color="Green" title="E50">A17</font></span>: 
 <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> (<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>)</span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="catalg_1.html#D3" target="_self" title="CATALG_1:def.3">Def5</a></span>;<br/>
<a NAME="E32:65"/><span class="kw">then </span>
( <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c16">g</font>,<font color="Maroon" title="c15">f</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">g</font> &amp; <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <span class="p2">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> (<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a>, <a class="ref" href="finseq_4.html#T17" title="FINSEQ_4:th.17">FINSEQ_4:17</a></span>;<br/>
<a NAME="E33:65"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A18</font></span>: 
<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c19">g9</font>,<font color="Maroon" title="c20">f9</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:65"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="txt" href="#E11:65"><span class="lab"><font color="Green" title="E40">A7</font></span></a>, <a class="txt" href="#E8:65"><span class="lab"><font color="Green" title="E38">A5</font></span></a>, <a class="txt" href="#E23:65"><span class="lab"><font color="Green" title="E47">A14</font></span></a>, <a class="txt" href="#E25:65"><span class="lab"><font color="Green" title="E48">A15</font></span></a>, <a class="txt" href="#E15:65"><span class="lab"><font color="Green" title="E42">A9</font></span></a>, <a class="txt" href="#E17:65"><span class="lab"><font color="Green" title="E44">A11</font></span></a>, <a class="ref" href="msualg_3.html#T24" title="MSUALG_3:th.24">MSUALG_3:24</a></span>;<br/>
<a NAME="E34:65"/>
( <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c16">g</font>,<font color="Maroon" title="c15">f</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">f</font> &amp; <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <span class="p2">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">c</font>)</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> (<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font>) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:65"><span class="lab"><font color="Green" title="E50">A17</font></span></a>, <a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a>, <a class="ref" href="finseq_4.html#T17" title="FINSEQ_4:th.17">FINSEQ_4:17</a></span>;<br/>
<a NAME="E35:65"/><span class="kw">then </span>
<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c19">g9</font>,<font color="Maroon" title="c20">f9</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:65"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="txt" href="#E11:65"><span class="lab"><font color="Green" title="E40">A7</font></span></a>, <a class="txt" href="#E8:65"><span class="lab"><font color="Green" title="E38">A5</font></span></a>, <a class="txt" href="#E23:65"><span class="lab"><font color="Green" title="E47">A14</font></span></a>, <a class="txt" href="#E25:65"><span class="lab"><font color="Green" title="E48">A15</font></span></a>, <a class="txt" href="#E20:65"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="txt" href="#E21:65"><span class="lab"><font color="Green" title="E46">A13</font></span></a>, <a class="ref" href="msualg_3.html#T24" title="MSUALG_3:th.24">MSUALG_3:24</a></span>;<br/>
<span class="kw">hence </span><a NAME="E36:65"/>
<font color="Maroon" title="c18">H</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">f</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:65"><span class="lab"><font color="Green" title="E48">A15</font></span></a>, <a class="txt" href="#E33:65"><span class="lab"><font color="Green" title="E51">A18</font></span></a>, <a class="txt" href="#E30:65"><span class="lab"><font color="Green" title="E49">A16</font></span></a>, <a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</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/>


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