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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="altcat_1.html#V2" title="ALTCAT_1:attr.2">transitive</a>   <a href="altcat_1.html#V12" title="ALTCAT_1:attr.12">with_units</a>   <a href="altcat_1.html#L2" title="ALTCAT_1:struct.2">AltCatStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">F</font> being   <a href="functor0.html#V6" title="FUNCTOR0:attr.6">reflexive</a>   <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>  st <font color="Olive" title="b1">F</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>  &amp; <font color="Olive" title="b1">F</font> is  <a href="functor0.html#V14" title="FUNCTOR0:attr.14">comp-reversing</a>  &amp; <font color="Olive" title="b1">F</font> is  <a href="functor0.html#V11" title="FUNCTOR0:attr.11">Contravariant</a>  &amp; <font color="Olive" title="b1">F</font> is  <a href="functor0.html#V7" title="FUNCTOR0:attr.7">coreflexive</a>  holds <br/><font color="Olive" title="b1">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  is  <a href="functor0.html#V14" title="FUNCTOR0:attr.14">comp-reversing</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">F</font> be   <a href="functor0.html#V6" title="FUNCTOR0:attr.6">reflexive</a>   <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</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="c3">F</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>  &amp; <font color="Maroon" title="c3">F</font> is  <a href="functor0.html#V14" title="FUNCTOR0:attr.14">comp-reversing</a>  &amp; <font color="Maroon" title="c3">F</font> is  <a href="functor0.html#V11" title="FUNCTOR0:attr.11">Contravariant</a>  &amp; <font color="Maroon" title="c3">F</font> is  <a href="functor0.html#V7" title="FUNCTOR0:attr.7">coreflexive</a>  implies <font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  is  <a href="functor0.html#V14" title="FUNCTOR0:attr.14">comp-reversing</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:112"/><span class="lab"><font color="Green" title="E75">A1</font></span>: 
( <font color="Maroon" title="c3">F</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>  &amp; <font color="Maroon" title="c3">F</font> is  <a href="functor0.html#V14" title="FUNCTOR0:attr.14">comp-reversing</a>  &amp; <font color="Maroon" title="c3">F</font> is  <a href="functor0.html#V11" title="FUNCTOR0:attr.11">Contravariant</a>  &amp; <font color="Maroon" title="c3">F</font> is  <a href="functor0.html#V7" title="FUNCTOR0:attr.7">coreflexive</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="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  is  <a href="functor0.html#V14" title="FUNCTOR0:attr.14">comp-reversing</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c4">G</font> = <font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> ;<br/>
<a NAME="E2:112"/><span class="lab"><font color="Green" title="E76">A2</font></span>: 
<font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  is  <a href="functor0.html#V11" title="FUNCTOR0:attr.11">Contravariant</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="ref" href="functor0.html#T39" target="_self" title="FUNCTOR0:th.39">Th40</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">H</font> = <font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  as   <a href="functor0.html#V6" title="FUNCTOR0:attr.6">reflexive</a>   <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="ref" href="functor0.html#T35" target="_self" title="FUNCTOR0:th.35">Th36</a>, <a class="ref" href="functor0.html#T36" target="_self" title="FUNCTOR0:th.36">Th37</a></span>;<br/>
<a NAME="E4:112"/><span class="lab"><font color="Green" title="E77">A3</font></span>: 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="ref" href="functor0.html#D38" target="_self" title="FUNCTOR0:def.38">Def39</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c6">ff</font> being    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of  the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font>, the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font><span class="kw"> such that </span><br/><a NAME="E6:112"/><span class="lab"><font color="Green" title="E78">A4</font></span>: 
<font color="Maroon" title="c6">ff</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c3">F</font>
 <span class="kw">and </span><br/><a NAME="E7:112"/><span class="lab"><font color="Green" title="E79">A5</font></span>: 
 the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">ff</font> <a href="msualg_3.html#K4" title="MSUALG_3:func.4">""</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="ref" href="functor0.html#D38" target="_self" title="FUNCTOR0:def.38">Def39</a></span>;<br/>
<a NAME="E8:112"/><span class="lab"><font color="Green" title="E80">A6</font></span>: 
<font color="Maroon" title="c3">F</font> is  <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="ref" href="functor0.html#D35" target="_self" title="FUNCTOR0:def.35">Def36</a></span>;<br/>
<a NAME="E9:112"/><span class="kw">then </span>
<font color="Maroon" title="c3">F</font> is  <a href="functor0.html#V4" title="FUNCTOR0:attr.4">one-to-one</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D33" target="_self" title="FUNCTOR0:def.33">Def34</a></span>;<br/>
<a NAME="E10:112"/><span class="kw">then </span><span class="lab"><font color="Green" title="E81">A7</font></span>: 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">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="functor0.html#D6" target="_self" title="FUNCTOR0:def.6">Def7</a></span>;<br/>
<a NAME="E11:112"/>
<font color="Maroon" title="c3">F</font> is  <a href="functor0.html#V17" title="FUNCTOR0:attr.17">faithful</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:112"><span class="lab"><font color="Green" title="E80">A6</font></span></a>, <a class="ref" href="functor0.html#D33" target="_self" title="FUNCTOR0:def.33">Def34</a></span>;<br/>
<a NAME="E12:112"/><span class="kw">then </span><span class="lab"><font color="Green" title="E82">A8</font></span>: 
 the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c3">F</font> is  <a href="msualg_3.html#V1" title="MSUALG_3:attr.1">"1-1"</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D30" target="_self" title="FUNCTOR0:def.30">Def31</a></span>;<br/>
<a NAME="E13:112"/>
<font color="Maroon" title="c3">F</font> is  <a href="functor0.html#V20" title="FUNCTOR0:attr.20">surjective</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="ref" href="functor0.html#D35" target="_self" title="FUNCTOR0:def.35">Def36</a></span>;<br/>
<a NAME="E14:112"/><span class="kw">then </span>
<font color="Maroon" title="c3">F</font> is  <a href="functor0.html#V18" title="FUNCTOR0:attr.18">full</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D34" target="_self" title="FUNCTOR0:def.34">Def35</a></span>;<br/>
<a NAME="E15:112"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A9</font></span>: 
 ex <font color="Olive" title="b1">f</font> being    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of  the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font>, the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> st <br/>( <font color="Olive" title="b1">f</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c3">F</font> &amp; <font color="Olive" title="b1">f</font> is  <a href="msualg_3.html#V2" title="MSUALG_3:attr.2">"onto"</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D32" target="_self" title="FUNCTOR0:def.32">Def33</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c7">o1</font>, <font color="Maroon" title="c8">o2</font>, <font color="Maroon" title="c9">o3</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">B</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="functor0.html#D22" target="_self" title="FUNCTOR0:def.22">FUNCTOR0:def 22</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="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  for <font color="Olive" title="b1">f</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font><br/>  for <font color="Olive" title="b2">g</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font>  ex <font color="Olive" title="b3">f9</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span> ex <font color="Olive" title="b4">g9</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span> st <br/>( <font color="Olive" title="b3">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">f</font> &amp; <font color="Olive" title="b4">g9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">g</font> &amp; <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">g</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f9</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Olive" title="b4">g9</font> ) )</span><br/>

<span class="kw">assume </span><a NAME="E16:112"/><span class="lab"><font color="Green" title="E84">A10</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  for <font color="Olive" title="b1">f</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font><br/>  for <font color="Olive" title="b2">g</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font>  ex <font color="Olive" title="b3">f9</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span> ex <font color="Olive" title="b4">g9</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span> st <br/>( <font color="Olive" title="b3">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">f</font> &amp; <font color="Olive" title="b4">g9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">g</font> &amp; <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">g</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f9</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Olive" title="b4">g9</font> ) )</span><br/>

<a NAME="E17:112"/><span class="kw">then </span><span class="lab"><font color="Green" title="E85">A11</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:112"><span class="lab"><font color="Green" title="E76">A2</font></span></a>, <a class="ref" href="functor0.html#D19" target="_self" title="FUNCTOR0:def.19">Def20</a></span>;<br/>
<span class="kw">assume </span><a NAME="E18:112"/><span class="lab"><font color="Green" title="E86">A12</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font><br/>  for <font color="Olive" title="b2">g</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font>  ex <font color="Olive" title="b3">f9</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span> ex <font color="Olive" title="b4">g9</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span> st <br/>( <font color="Olive" title="b3">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">f</font> &amp; <font color="Olive" title="b4">g9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">g</font> &amp; <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">g</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f9</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Olive" title="b4">g9</font> )</span><br/>

<a NAME="E19:112"/><span class="kw">then </span><span class="lab"><font color="Green" title="E87">A13</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:112"><span class="lab"><font color="Green" title="E76">A2</font></span></a>, <a class="ref" href="functor0.html#D19" target="_self" title="FUNCTOR0:def.19">Def20</a></span>;<br/>
<a NAME="E20:112"/><span class="lab"><font color="Green" title="E88">A14</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:112"><span class="lab"><font color="Green" title="E84">A10</font></span></a>, <a class="txt" href="#E18:112"><span class="lab"><font color="Green" title="E86">A12</font></span></a>, <a class="ref" href="altcat_1.html#D2" title="ALTCAT_1:def.2">ALTCAT_1:def 2</a></span>;<br/>
<a NAME="E21:112"/><span class="kw">then </span><span class="lab"><font color="Green" title="E89">A15</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:112"><span class="lab"><font color="Green" title="E76">A2</font></span></a>, <a class="ref" href="functor0.html#D19" target="_self" title="FUNCTOR0:def.19">Def20</a></span>;<br/>
<a NAME="E22:112"/><span class="kw">then </span><span class="lab"><font color="Green" title="E90">A16</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="ref" href="functor0.html#D19" target="_self" title="FUNCTOR0:def.19">Def20</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c10">f</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</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">g</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font>  ex <font color="Olive" title="b2">f9</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span> ex <font color="Olive" title="b3">g9</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span> st <br/>( <font color="Olive" title="b2">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">f</font> &amp; <font color="Olive" title="b3">g9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">g</font> &amp; <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">g</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c10">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f9</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Olive" title="b3">g9</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c11">g</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">f9</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span> ex <font color="Olive" title="b2">g9</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span> st <br/>( <font color="Olive" title="b1">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">f</font> &amp; <font color="Olive" title="b2">g9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">g</font> &amp; <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c10">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f9</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Olive" title="b2">g9</font> )</span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c12">K</font> = <font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  as   <a href="functor0.html#V11" title="FUNCTOR0:attr.11">Contravariant</a>   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="ref" href="functor0.html#T39" target="_self" title="FUNCTOR0:th.39">Th40</a></span>;<br/>
<a NAME="E24:112"/>
<font color="Maroon" title="c12">K</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Maroon" title="c10">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K7" title="FUNCTOR0:func.7">Morph-Map</a> (<font color="Maroon" title="c12">K</font>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:112"><span class="lab"><font color="Green" title="E84">A10</font></span></a>, <a class="txt" href="#E17:112"><span class="lab"><font color="Green" title="E85">A11</font></span></a>, <a class="ref" href="functor0.html#D16" target="_self" title="FUNCTOR0:def.16">Def17</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c13">f9</font> = <span class="p1">(<span class="default"><a href="functor0.html#K7" title="FUNCTOR0:func.7">Morph-Map</a> (<font color="Maroon" title="c12">K</font>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">f</font> as   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span> ;<br/>
<a NAME="E26:112"/>
<font color="Maroon" title="c12">K</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Maroon" title="c11">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K7" title="FUNCTOR0:func.7">Morph-Map</a> (<font color="Maroon" title="c12">K</font>,<font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:112"><span class="lab"><font color="Green" title="E86">A12</font></span></a>, <a class="txt" href="#E19:112"><span class="lab"><font color="Green" title="E87">A13</font></span></a>, <a class="ref" href="functor0.html#D16" target="_self" title="FUNCTOR0:def.16">Def17</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c14">g9</font> = <span class="p1">(<span class="default"><a href="functor0.html#K7" title="FUNCTOR0:func.7">Morph-Map</a> (<font color="Maroon" title="c12">K</font>,<font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">g</font> as   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c13">f9</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">g9</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span> st <br/>( <font color="Maroon" title="c13">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">f</font> &amp; <font color="Olive" title="b1">g9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">g</font> &amp; <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c10">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">f9</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Olive" title="b1">g9</font> )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c14">g9</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="c13">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">f</font> &amp; <font color="Maroon" title="c14">g9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">g</font> &amp; <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c10">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">f9</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c14">g9</font> )</span><br/>

<span class="kw">thus </span><a NAME="E28:112"/>
<font color="Maroon" title="c13">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">f</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="c14">g9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">g</font> &amp; <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c10">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">f9</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c14">g9</font> )</span><br/>

<span class="kw">thus </span><a NAME="E29:112"/>
<font color="Maroon" title="c14">g9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">g</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c10">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">f9</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c14">g9</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c15">g99</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span></span>)</span>, <font color="Maroon" title="c16">f99</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span></span>)</span><span class="kw"> such that </span><br/><a NAME="E31:112"/><span class="lab"><font color="Green" title="E91">A17</font></span>: 
<font color="Maroon" title="c15">g99</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c3">F</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">g9</font>
 <span class="kw">and </span><br/><a NAME="E32:112"/><span class="lab"><font color="Green" title="E92">A18</font></span>: 
<font color="Maroon" title="c16">f99</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c3">F</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">f9</font>
 <span class="kw">and </span><br/><a NAME="E33:112"/><span class="lab"><font color="Green" title="E93">A19</font></span>: 
<span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c3">F</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">f9</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c14">g9</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">g99</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c16">f99</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="txt" href="#E17:112"><span class="lab"><font color="Green" title="E85">A11</font></span></a>, <a class="txt" href="#E19:112"><span class="lab"><font color="Green" title="E87">A13</font></span></a>, <a class="ref" href="functor0.html#D22" target="_self" title="FUNCTOR0:def.22">Def23</a></span>;<br/>
<a NAME="E34:112"/><span class="lab"><font color="Green" title="E94">A20</font></span>: 
<font color="Maroon" title="c11">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">g99</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="txt" href="#E18:112"><span class="lab"><font color="Green" title="E86">A12</font></span></a>, <a class="txt" href="#E31:112"><span class="lab"><font color="Green" title="E91">A17</font></span></a>, <a class="ref" href="functor0.html#T41" target="_self" title="FUNCTOR0:th.41">Th42</a></span>;<br/>
<a NAME="E35:112"/><span class="lab"><font color="Green" title="E95">A21</font></span>: 
<font color="Maroon" title="c10">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">f99</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="txt" href="#E16:112"><span class="lab"><font color="Green" title="E84">A10</font></span></a>, <a class="txt" href="#E32:112"><span class="lab"><font color="Green" title="E92">A18</font></span></a>, <a class="ref" href="functor0.html#T41" target="_self" title="FUNCTOR0:th.41">Th42</a></span>;<br/>
<a NAME="E36:112"/><span class="lab"><font color="Green" title="E96">A22</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/>
<a NAME="E37:112"/><span class="lab"><font color="Green" title="E97">A23</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/>
<a NAME="E38:112"/><span class="kw">then </span><span class="lab"><font color="Green" title="E98">A24</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</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="E39:112"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E40:112"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c3">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/>
<a NAME="E41:112"/><span class="kw">then </span><span class="lab"><font color="Green" title="E99">A25</font></span>: 
 <a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c3">F</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span>) 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="txt" href="#E12:112"><span class="lab"><font color="Green" title="E82">A8</font></span></a>, <a class="ref" href="msualg_3.html#D2" title="MSUALG_3:def.2">MSUALG_3:def 2</a></span>;<br/>
<a NAME="E42:112"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:112"><span class="lab"><font color="Green" title="E96">A22</font></span></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E100">A26</font></span>: <span class="p1">(<span class="default"> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> = 
 the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T13" title="FUNCT_1:th.13">FUNCT_1:13</a></span>
<br/>.= 
 the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="ref" href="functor0.html#T23" target="_self" title="FUNCTOR0:th.23">Th24</a></span>
<br/>.= 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_1.html#D1" title="ALTCAT_1:def.1">ALTCAT_1:def 1</a></span>
;<br/>
<a NAME="E44:112"/>
 <a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c3">F</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:112"><span class="lab"><font color="Green" title="E78">A4</font></span></a>, <a class="txt" href="#E36:112"><span class="lab"><font color="Green" title="E96">A22</font></span></a>, <a class="ref" href="pboole.html#D15" title="PBOOLE:def.15">PBOOLE:def 15</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E101">A27</font></span>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c3">F</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span>)</span>)</span> = 
 the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:112"><span class="lab"><font color="Green" title="E90">A16</font></span></a>, <a class="txt" href="#E43:112"><span class="lab"><font color="Green" title="E100">A26</font></span></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>
<br/>.= 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_1.html#D1" title="ALTCAT_1:def.1">ALTCAT_1:def 1</a></span>
;<br/>
<span class="lab"><font color="Green" title="E102">A28</font></span>: <span class="p1">(<span class="default"> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> = 
 the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">H</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:112"><span class="lab"><font color="Green" title="E98">A24</font></span></a>, <a class="ref" href="funct_1.html#T13" title="FUNCT_1:th.13">FUNCT_1:13</a></span>
<br/>.= 
 the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:112"><span class="lab"><font color="Green" title="E76">A2</font></span></a>, <a class="ref" href="functor0.html#T23" target="_self" title="FUNCTOR0:th.23">Th24</a></span>
<br/>.= 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_1.html#D1" title="ALTCAT_1:def.1">ALTCAT_1:def 1</a></span>
;<br/>
<a NAME="E47:112"/>
 the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> is    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of  the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font>, the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D4" target="_self" title="FUNCTOR0:def.4">Def5</a></span>;<br/>
<a NAME="E48:112"/><span class="kw">then </span>
 <a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:112"><span class="lab"><font color="Green" title="E97">A23</font></span></a>, <a class="ref" href="pboole.html#D15" title="PBOOLE:def.15">PBOOLE:def 15</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E103">A29</font></span>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> = 
 the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:112"><span class="lab"><font color="Green" title="E89">A15</font></span></a>, <a class="txt" href="#E46:112"><span class="lab"><font color="Green" title="E102">A28</font></span></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>
<br/>.= 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_1.html#D1" title="ALTCAT_1:def.1">ALTCAT_1:def 1</a></span>
;<br/>
<span class="lab"><font color="Green" title="E104">A30</font></span>:  <a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>) = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">ff</font> <a href="msualg_3.html#K4" title="MSUALG_3:func.4">""</a></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:112"><span class="lab"><font color="Green" title="E77">A3</font></span></a>, <a class="txt" href="#E7:112"><span class="lab"><font color="Green" title="E79">A5</font></span></a>, <a class="txt" href="#E38:112"><span class="lab"><font color="Green" title="E98">A24</font></span></a>, <a class="ref" href="funct_1.html#T13" title="FUNCT_1:th.13">FUNCT_1:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">ff</font> <a href="msualg_3.html#K4" title="MSUALG_3:func.4">""</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:112"><span class="lab"><font color="Green" title="E76">A2</font></span></a>, <a class="ref" href="functor0.html#T23" target="_self" title="FUNCTOR0:th.23">Th24</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c3">F</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span>)</span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:112"><span class="lab"><font color="Green" title="E78">A4</font></span></a>, <a class="txt" href="#E12:112"><span class="lab"><font color="Green" title="E82">A8</font></span></a>, <a class="txt" href="#E15:112"><span class="lab"><font color="Green" title="E83">A9</font></span></a>, <a class="txt" href="#E36:112"><span class="lab"><font color="Green" title="E96">A22</font></span></a>, <a class="ref" href="msualg_3.html#D4" title="MSUALG_3:def.4">MSUALG_3:def 4</a></span>
;<br/>
<span class="lab"><font color="Green" title="E105">A31</font></span>:  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">H</font></span>)</span> = 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a>  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">H</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D36" target="_self" title="FUNCTOR0:def.36">Def37</a></span>
<br/>.= 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="ref" href="functor0.html#D38" target="_self" title="FUNCTOR0:def.38">Def39</a></span>
<br/>.= 
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K11" title="FUNCOP_1:func.11">rng</a>  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:112"><span class="lab"><font color="Green" title="E81">A7</font></span></a>, <a class="ref" href="funct_1.html#T39" title="FUNCT_1:th.39">FUNCT_1:39</a></span>
<br/>.= 
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:112"><span class="lab"><font color="Green" title="E77">A3</font></span></a>, <a class="txt" href="#E10:112"><span class="lab"><font color="Green" title="E81">A7</font></span></a>, <a class="ref" href="funct_1.html#T33" title="FUNCT_1:th.33">FUNCT_1:33</a></span>
<br/>.= 
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
<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="E52:112"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c7">o1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/>
<a NAME="E53:112"/><span class="kw">then </span><span class="lab"><font color="Green" title="E106">A32</font></span>: 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c7">o1</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="c7">o1</font>,<font color="Maroon" title="c7">o1</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="#E51:112"><span class="lab"><font color="Green" title="E105">A31</font></span></a>, <a class="ref" href="funct_1.html#T18" title="FUNCT_1:th.18">FUNCT_1:18</a></span>;<br/>
<span class="lab"><font color="Green" title="E107">A33</font></span>: <font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#T33" target="_self" title="FUNCTOR0:th.33">Th34</a></span>
<br/>.= 
<font color="Maroon" title="c7">o1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E53:112"><span class="lab"><font color="Green" title="E106">A32</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>
;<br/>
<a NAME="E55:112"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c8">o2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/>
<a NAME="E56:112"/><span class="kw">then </span><span class="lab"><font color="Green" title="E108">A34</font></span>: 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c8">o2</font>,<font color="Maroon" title="c8">o2</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">o2</font>,<font color="Maroon" title="c8">o2</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="#E51:112"><span class="lab"><font color="Green" title="E105">A31</font></span></a>, <a class="ref" href="funct_1.html#T18" title="FUNCT_1:th.18">FUNCT_1:18</a></span>;<br/>
<span class="lab"><font color="Green" title="E109">A35</font></span>: <font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c8">o2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#T33" target="_self" title="FUNCTOR0:th.33">Th34</a></span>
<br/>.= 
<font color="Maroon" title="c8">o2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E56:112"><span class="lab"><font color="Green" title="E108">A34</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>
;<br/>
<a NAME="E58:112"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">o3</font>,<font color="Maroon" title="c9">o3</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/>
<a NAME="E59:112"/><span class="kw">then </span><span class="lab"><font color="Green" title="E110">A36</font></span>: 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c9">o3</font>,<font color="Maroon" title="c9">o3</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">o3</font>,<font color="Maroon" title="c9">o3</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="#E51:112"><span class="lab"><font color="Green" title="E105">A31</font></span></a>, <a class="ref" href="funct_1.html#T18" title="FUNCT_1:th.18">FUNCT_1:18</a></span>;<br/>
<span class="lab"><font color="Green" title="E111">A37</font></span>: <font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#T33" target="_self" title="FUNCTOR0:th.33">Th34</a></span>
<br/>.= 
<font color="Maroon" title="c9">o3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E59:112"><span class="lab"><font color="Green" title="E110">A36</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>
;<br/>
<a NAME="E61:112"/>
<span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c10">f</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:112"><span class="lab"><font color="Green" title="E88">A14</font></span></a>, <a class="txt" href="#E49:112"><span class="lab"><font color="Green" title="E103">A29</font></span></a>, <a class="ref" href="funct_1.html#D3" title="FUNCT_1:def.3">FUNCT_1:def 3</a></span>;<br/>
<a NAME="E62:112"/><span class="kw">then </span><span class="lab"><font color="Green" title="E112">A38</font></span>: 
<span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c10">f</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c3">F</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:112"><span class="lab"><font color="Green" title="E99">A25</font></span></a>, <a class="txt" href="#E50:112"><span class="lab"><font color="Green" title="E104">A30</font></span></a>, <a class="ref" href="funct_1.html#T33" title="FUNCT_1:th.33">FUNCT_1:33</a></span>;<br/>
<a NAME="E63:112"/>
<span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c3">F</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c10">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c3">F</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c9">o3</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">f9</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c14">g9</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="txt" href="#E20:112"><span class="lab"><font color="Green" title="E88">A14</font></span></a>, <a class="txt" href="#E33:112"><span class="lab"><font color="Green" title="E93">A19</font></span></a>, <a class="txt" href="#E34:112"><span class="lab"><font color="Green" title="E94">A20</font></span></a>, <a class="txt" href="#E35:112"><span class="lab"><font color="Green" title="E95">A21</font></span></a>, <a class="txt" href="#E54:112"><span class="lab"><font color="Green" title="E107">A33</font></span></a>, <a class="txt" href="#E57:112"><span class="lab"><font color="Green" title="E109">A35</font></span></a>, <a class="txt" href="#E60:112"><span class="lab"><font color="Green" title="E111">A37</font></span></a>, <a class="ref" href="functor0.html#T41" target="_self" title="FUNCTOR0:th.41">Th42</a></span>;<br/>
<span class="kw">hence </span><a NAME="E64:112"/>
<span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c9">o3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c10">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">f9</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c14">g9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:112"><span class="lab"><font color="Green" title="E99">A25</font></span></a>, <a class="txt" href="#E45:112"><span class="lab"><font color="Green" title="E101">A27</font></span></a>, <a class="txt" href="#E62:112"><span class="lab"><font color="Green" title="E112">A38</font></span></a>, <a class="ref" href="funct_1.html#D4" title="FUNCT_1:def.4">FUNCT_1:def 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/>


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