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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#V7" title="FUNCTOR0:attr.7">coreflexive</a>  &amp; <font color="Olive" title="b1">F</font> is  <a href="functor0.html#V10" title="FUNCTOR0:attr.10">Covariant</a>  holds <br/> for <font color="Olive" title="b2">o1</font>, <font color="Olive" title="b3">o2</font> being   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">B</font><br/>  for <font color="Olive" title="b4">m</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b2">o1</font>,<font color="Olive" title="b3">o2</font>  st <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b2">o1</font>,<font color="Olive" title="b3">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>  holds <br/><span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Olive" title="b1">F</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">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="Olive" title="b2">o1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">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="Olive" title="b3">o2</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="Olive" title="b1">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span>,<font color="Olive" title="b2">o1</font>,<font color="Olive" title="b3">o2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">m</font></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#V7" title="FUNCTOR0:attr.7">coreflexive</a>  &amp; <font color="Maroon" title="c3">F</font> is  <a href="functor0.html#V10" title="FUNCTOR0:attr.10">Covariant</a>  implies  for <font color="Olive" title="b1">o1</font>, <font color="Olive" title="b2">o2</font> being   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">B</font><br/>  for <font color="Olive" title="b3">m</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">o1</font>,<font color="Olive" title="b2">o2</font>  st <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b1">o1</font>,<font color="Olive" title="b2">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>  holds <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="Olive" title="b1">o1</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="Olive" title="b2">o2</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="Olive" title="b1">o1</font>,<font color="Olive" title="b2">o2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">m</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:109"/><span class="lab"><font color="Green" title="E72">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#V7" title="FUNCTOR0:attr.7">coreflexive</a>  &amp; <font color="Maroon" title="c3">F</font> is  <a href="functor0.html#V10" title="FUNCTOR0:attr.10">Covariant</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">o1</font>, <font color="Olive" title="b2">o2</font> being   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">B</font><br/>  for <font color="Olive" title="b3">m</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">o1</font>,<font color="Olive" title="b2">o2</font>  st <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b1">o1</font>,<font color="Olive" title="b2">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>  holds <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="Olive" title="b1">o1</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="Olive" title="b2">o2</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="Olive" title="b1">o1</font>,<font color="Olive" title="b2">o2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">m</font></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="E2:109"/><span class="lab"><font color="Green" title="E73">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#V10" title="FUNCTOR0:attr.10">Covariant</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:109"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="functor0.html#T38" target="_self" title="FUNCTOR0:th.38">Th39</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="#E1:109"><span class="lab"><font color="Green" title="E72">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="E4:109"/><span class="lab"><font color="Green" title="E74">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="#E1:109"><span class="lab"><font color="Green" title="E72">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">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><span class="kw"> such that </span><br/><a NAME="E6:109"/><span class="lab"><font color="Green" title="E75">A4</font></span>: 
<font color="Maroon" title="c6">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>
 <span class="kw">and </span><br/><a NAME="E7:109"/><span class="lab"><font color="Green" title="E76">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">f</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="#E1:109"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="functor0.html#D38" target="_self" title="FUNCTOR0:def.38">Def39</a></span>;<br/>
<a NAME="E8:109"/>
<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="#E1:109"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="functor0.html#D35" target="_self" title="FUNCTOR0:def.35">Def36</a></span>;<br/>
<a NAME="E9:109"/><span class="kw">then </span>
<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="ref" href="functor0.html#D33" target="_self" title="FUNCTOR0:def.33">Def34</a></span>;<br/>
<a NAME="E10:109"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A6</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="E11:109"/>
<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="#E1:109"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="functor0.html#D35" target="_self" title="FUNCTOR0:def.35">Def36</a></span>;<br/>
<a NAME="E12:109"/><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="E13:109"/><span class="kw">then </span><span class="lab"><font color="Green" title="E78">A7</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> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <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">  for <font color="Olive" title="b1">m</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>  st <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>  holds <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="c7">o1</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> <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="c8">o2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">m</font></span><br/><span class="kw">let </span><font color="Maroon" title="c9">m</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"> ( <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>  implies <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="c7">o1</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> <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="c8">o2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">m</font> )</span><br/>



<span class="kw">assume </span><a NAME="E14:109"/><span class="lab"><font color="Green" title="E79">A8</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"> <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="c7">o1</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> <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="c8">o2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">m</font></span><br/>

<a NAME="E15:109"/><span class="lab"><font color="Green" title="E80">A9</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="c7">o1</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><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="E16:109"/><span class="lab"><font color="Green" title="E81">A10</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="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="E17:109"/><span class="kw">then </span><span class="lab"><font color="Green" title="E82">A11</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="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>  <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="E18:109"/>
 <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="E19:109"/><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="c7">o1</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><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="E20:109"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A12</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="c7">o1</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>) 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="#E10:109"><span class="lab"><font color="Green" title="E77">A6</font></span></a>, <a class="ref" href="msualg_3.html#D2" title="MSUALG_3:def.2">MSUALG_3:def 2</a></span>;<br/>
<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="c8">o2</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="c8">o2</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:109"><span class="lab"><font color="Green" title="E82">A11</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"><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 class="p1">(<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="kw">by</span> <span class="lab"><a class="txt" href="#E2:109"><span class="lab"><font color="Green" title="E73">A2</font></span></a>, <a class="ref" href="functor0.html#T22" target="_self" title="FUNCTOR0:th.22">Th23</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="c5">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">o1</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>
<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="E22:109"/><span class="kw">then </span><span class="lab"><font color="Green" title="E84">A13</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="c8">o2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</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="#E2:109"><span class="lab"><font color="Green" title="E73">A2</font></span></a>, <a class="txt" href="#E14:109"><span class="lab"><font color="Green" title="E79">A8</font></span></a>, <a class="ref" href="functor0.html#D18" target="_self" title="FUNCTOR0:def.18">Def19</a></span>;<br/>
<a NAME="E23:109"/>
 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="E24:109"/><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="c8">o2</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="c8">o2</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="c8">o2</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="#E16:109"><span class="lab"><font color="Green" title="E81">A10</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="E85">A14</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="c8">o2</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="c8">o2</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:109"><span class="lab"><font color="Green" title="E84">A13</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="c8">o2</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="E86">A15</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="c8">o2</font>) = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</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="c8">o2</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:109"><span class="lab"><font color="Green" title="E74">A3</font></span></a>, <a class="txt" href="#E7:109"><span class="lab"><font color="Green" title="E76">A5</font></span></a>, <a class="txt" href="#E17:109"><span class="lab"><font color="Green" title="E82">A11</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">f</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="c7">o1</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="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:109"><span class="lab"><font color="Green" title="E73">A2</font></span></a>, <a class="ref" href="functor0.html#T22" target="_self" title="FUNCTOR0:th.22">Th23</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="c7">o1</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#K2" title="FUNCT_1:func.2">"</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:109"><span class="lab"><font color="Green" title="E75">A4</font></span></a>, <a class="txt" href="#E10:109"><span class="lab"><font color="Green" title="E77">A6</font></span></a>, <a class="txt" href="#E13:109"><span class="lab"><font color="Green" title="E78">A7</font></span></a>, <a class="txt" href="#E15:109"><span class="lab"><font color="Green" title="E80">A9</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="kw">thus </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="c7">o1</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> <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="c8">o2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">m</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c3">F</font>,<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 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="c8">o2</font></span>)</span>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <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="c8">o2</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">m</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:109"><span class="lab"><font color="Green" title="E79">A8</font></span></a>, <a class="txt" href="#E25:109"><span class="lab"><font color="Green" title="E85">A14</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"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p3">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c3">F</font>,<span class="p4">(<span class="default"><span class="p5">(<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="p4">(<span class="default"><span class="p5">(<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>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">m</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:109"><span class="lab"><font color="Green" title="E83">A12</font></span></a>, <a class="txt" href="#E26:109"><span class="lab"><font color="Green" title="E86">A15</font></span></a>, <a class="ref" href="funct_1.html#T39" title="FUNCT_1:th.39">FUNCT_1:39</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<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>,<font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c8">o2</font>)</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">m</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:109"><span class="lab"><font color="Green" title="E83">A12</font></span></a>, <a class="txt" href="#E26:109"><span class="lab"><font color="Green" title="E86">A15</font></span></a>, <a class="ref" href="funct_1.html#T33" title="FUNCT_1:th.33">FUNCT_1:33</a></span>
<br/>.= 
<font color="Maroon" title="c9">m</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:109"><span class="lab"><font color="Green" title="E79">A8</font></span></a>, <a class="txt" href="#E25:109"><span class="lab"><font color="Green" title="E85">A14</font></span></a>, <a class="ref" href="funct_1.html#T18" title="FUNCT_1:th.18">FUNCT_1:18</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
