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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</font> be   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_2.html#V1" title="ALTCAT_2:attr.1">reflexive</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">G</font> being   <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><br/>  for <font color="Olive" title="b2">F</font> being   <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="c3">C</font><br/>  for <font color="Olive" title="b3">GI</font> being   <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><br/>  for <font color="Olive" title="b4">FI</font> being   <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="c3">C</font>,<font color="Maroon" title="c2">B</font>  st <font color="Olive" title="b2">F</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>  &amp; <font color="Olive" title="b1">G</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>  &amp;  <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Olive" title="b3">GI</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Olive" title="b3">GI</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">G</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  &amp;  <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Olive" title="b4">FI</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Olive" title="b4">FI</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">GI</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Olive" title="b4">FI</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">G</font> be   <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">  for <font color="Olive" title="b1">F</font> being   <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="c3">C</font><br/>  for <font color="Olive" title="b2">GI</font> being   <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><br/>  for <font color="Olive" title="b3">FI</font> being   <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="c3">C</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="Maroon" title="c4">G</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>  &amp;  <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Olive" title="b2">GI</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Olive" title="b2">GI</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  &amp;  <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Olive" title="b3">FI</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Olive" title="b3">FI</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">GI</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Olive" title="b3">FI</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">F</font> be   <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="c3">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">GI</font> being   <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><br/>  for <font color="Olive" title="b2">FI</font> being   <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="c3">C</font>,<font color="Maroon" title="c2">B</font>  st <font color="Maroon" title="c5">F</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>  &amp; <font color="Maroon" title="c4">G</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>  &amp;  <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Olive" title="b1">GI</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Olive" title="b1">GI</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  &amp;  <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Olive" title="b2">FI</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Olive" title="b2">FI</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">GI</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Olive" title="b2">FI</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">GI</font> be   <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>; <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">FI</font> being   <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="c3">C</font>,<font color="Maroon" title="c2">B</font>  st <font color="Maroon" title="c5">F</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>  &amp; <font color="Maroon" title="c4">G</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>  &amp;  <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c6">GI</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c6">GI</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  &amp;  <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Olive" title="b1">FI</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Olive" title="b1">FI</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">GI</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Olive" title="b1">FI</font></span><br/><span class="kw">let </span><font color="Maroon" title="c7">FI</font> be   <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="c3">C</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="c5">F</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>  &amp; <font color="Maroon" title="c4">G</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>  &amp;  <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c6">GI</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c6">GI</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  &amp;  <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c7">FI</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c7">FI</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  implies <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">GI</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c7">FI</font> )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:26"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
<font color="Maroon" title="c5">F</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> 
 <span class="kw">and </span><br/><a NAME="E2:26"/><span class="lab"><font color="Green" title="E13">A2</font></span>: 
<font color="Maroon" title="c4">G</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> 
 <span class="kw">and </span><br/><a NAME="E3:26"/><span class="lab"><font color="Green" title="E14">A3</font></span>: 
 <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c6">GI</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c6">GI</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> 
 <span class="kw">and </span><br/><a NAME="E4:26"/><span class="lab"><font color="Green" title="E15">A4</font></span>: 
 <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c7">FI</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c7">FI</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</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"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">GI</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c7">FI</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c8">MF</font> =  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c5">F</font> as    <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="c3">C</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="c5">F</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D4" title="FUNCTOR0:def.4">FUNCTOR0:def 4</a></span>;<br/>
<a NAME="E6:26"/><span class="lab"><font color="Green" title="E16">A5</font></span>: 
<font color="Maroon" title="c8">MF</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="txt" href="#E1:26"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="functor1.html#T5" target="_self" title="FUNCTOR1:th.5">Th6</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">OG</font> =  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">CB</font> = <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>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">CA</font> = <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>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">OGI</font> =  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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="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="txt" href="#E2:26"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="functor1.html#T2" target="_self" title="FUNCTOR1:th.2">Th3</a>, <a class="ref" href="functor1.html#T5" target="_self" title="FUNCTOR1:th.5">Th6</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">CC</font> = <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="c3">C</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">OF</font> =  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c15">OFI</font> =  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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="c3">C</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<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="txt" href="#E1:26"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="functor1.html#T2" target="_self" title="FUNCTOR1:th.2">Th3</a>, <a class="ref" href="functor1.html#T5" target="_self" title="FUNCTOR1:th.5">Th6</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c16">MFG</font> =  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> as    <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="c3">C</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="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D4" title="FUNCTOR0:def.4">FUNCTOR0:def 4</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">OG</font> =  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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="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> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c18">OFG</font> =  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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="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="c3">C</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c19">MG</font> =  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c4">G</font> as    <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="c4">G</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D4" title="FUNCTOR0:def.4">FUNCTOR0:def 4</a></span>;<br/>
<a NAME="E13:26"/><span class="lab"><font color="Green" title="E17">A6</font></span>: 
<font color="Maroon" title="c19">MG</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="txt" href="#E2:26"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="functor1.html#T5" target="_self" title="FUNCTOR1:th.5">Th6</a></span>;<br/>
<a NAME="E14:26"/>
<font color="Maroon" title="c5">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="#E1:26"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="functor0.html#D35" title="FUNCTOR0:def.35">FUNCTOR0:def 35</a></span>;<br/>
<a NAME="E15:26"/><span class="kw">then </span>
<font color="Maroon" title="c5">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" title="FUNCTOR0:def.34">FUNCTOR0:def 34</a></span>;<br/>
<a NAME="E16:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A7</font></span>: 
 ex <font color="Olive" title="b1">mf</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="c2">B</font>, the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c3">C</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="c5">F</font> st <br/>( <font color="Olive" title="b1">mf</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="c5">F</font> &amp; <font color="Olive" title="b1">mf</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" title="FUNCTOR0:def.32">FUNCTOR0:def 32</a></span>;<br/>
<a NAME="E17:26"/>
<font color="Maroon" title="c5">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="#E1:26"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="functor0.html#D35" title="FUNCTOR0:def.35">FUNCTOR0:def 35</a></span>;<br/>
<a NAME="E18:26"/><span class="kw">then </span>
<font color="Maroon" title="c5">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" title="FUNCTOR0:def.33">FUNCTOR0:def 33</a></span>;<br/>
<a NAME="E19:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A8</font></span>: 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">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" title="FUNCTOR0:def.6">FUNCTOR0:def 6</a></span>;<br/>
<a NAME="E20:26"/><span class="lab"><font color="Green" title="E20">A9</font></span>: 
<font color="Maroon" title="c4">G</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="#E2:26"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="functor0.html#D35" title="FUNCTOR0:def.35">FUNCTOR0:def 35</a></span>;<br/>
<a NAME="E21:26"/><span class="kw">then </span>
<font color="Maroon" title="c4">G</font> is  <a href="functor0.html#V5" title="FUNCTOR0:attr.5">onto</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D34" title="FUNCTOR0:def.34">FUNCTOR0:def 34</a></span>;<br/>
<a NAME="E22:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A10</font></span>: 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D7" title="FUNCTOR0:def.7">FUNCTOR0:def 7</a></span>;<br/>
<a NAME="E23:26"/>
<font color="Maroon" title="c4">G</font> is  <a href="functor0.html#V18" title="FUNCTOR0:attr.18">full</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:26"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="ref" href="functor0.html#D34" title="FUNCTOR0:def.34">FUNCTOR0:def 34</a></span>;<br/>
<a NAME="E24:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A11</font></span>: 
 ex <font color="Olive" title="b1">mg</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="c4">G</font> st <br/>( <font color="Olive" title="b1">mg</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="c4">G</font> &amp; <font color="Olive" title="b1">mg</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" title="FUNCTOR0:def.32">FUNCTOR0:def 32</a></span>;<br/>
<a NAME="E25:26"/>
<font color="Maroon" title="c4">G</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="#E2:26"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="functor0.html#D35" title="FUNCTOR0:def.35">FUNCTOR0:def 35</a></span>;<br/>
<a NAME="E26:26"/><span class="kw">then </span>
<font color="Maroon" title="c4">G</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" title="FUNCTOR0:def.33">FUNCTOR0:def 33</a></span>;<br/>
<a NAME="E27:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A12</font></span>: 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</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" title="FUNCTOR0:def.6">FUNCTOR0:def 6</a></span>;<br/>
<a NAME="E28:26"/><span class="lab"><font color="Green" title="E24">A13</font></span>: 
<font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="functor1.html#T12" target="_self" title="FUNCTOR1:th.12">Th13</a></span>;<br/>
<a NAME="E29:26"/><span class="kw">then </span>
<font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font> is  <a href="functor0.html#V20" title="FUNCTOR0:attr.20">surjective</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D35" title="FUNCTOR0:def.35">FUNCTOR0:def 35</a></span>;<br/>
<a NAME="E30:26"/><span class="kw">then </span>
<font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</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" title="FUNCTOR0:def.34">FUNCTOR0:def 34</a></span>;<br/>
<a NAME="E31:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A14</font></span>: 
 ex <font color="Olive" title="b1">mfg</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="c3">C</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="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> st <br/>( <font color="Olive" title="b1">mfg</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> &amp; <font color="Olive" title="b1">mfg</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" title="FUNCTOR0:def.32">FUNCTOR0:def 32</a></span>;<br/>
<a NAME="E32:26"/><span class="lab"><font color="Green" title="E26">A15</font></span>: 
<font color="Maroon" title="c16">MFG</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="txt" href="#E28:26"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="ref" href="functor1.html#T5" target="_self" title="FUNCTOR1:th.5">Th6</a></span>;<br/>
<a NAME="E33:26"/><span class="lab"><font color="Green" title="E27">A16</font></span>: 
 the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c6">GI</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c7">FI</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c20">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="c3">C</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="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E2:26_1"/><span class="lab"><font color="Green" title="E28">A17</font></span>: 
<font color="Maroon" title="c20">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 <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:26_1"/><span class="lab"><font color="Green" title="E29">A18</font></span>: 
 the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <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="c20">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 <span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <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="#E28:26"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="ref" href="functor0.html#D38" title="FUNCTOR0:def.38">FUNCTOR0:def 38</a></span>;<br/>
<a NAME="E4:26_1"/><span class="lab"><font color="Green" title="E30">A19</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a>  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</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="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="txt" href="#E22:26"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="ref" href="funct_2.html#D3" title="FUNCT_2:def.3">FUNCT_2:def 3</a></span>;<br/>
<a NAME="E5:26_1"/>
 for <font color="Olive" title="b1">i</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c20">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="p2">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <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="c5">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span></span>)</span> <a href="pboole.html#K8" title="PBOOLE:func.8">**</a>  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c5">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> <font color="Olive" title="b1">i</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:26_1_1"/><span class="lab"><font color="Green" title="E31">A20</font></span>: 
(  ex <font color="Olive" title="b1">x1</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="c2">B</font>, the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c3">C</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="c5">F</font> st <br/>( <font color="Olive" title="b1">x1</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="c5">F</font> &amp;  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c5">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="Olive" title="b1">x1</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="c5">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> ) &amp;  ex <font color="Olive" title="b1">x1</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="c4">G</font> st <br/>( <font color="Olive" title="b1">x1</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="c4">G</font> &amp;  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</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="Olive" title="b1">x1</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="c4">G</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="#E1:26"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="functor0.html#D38" title="FUNCTOR0:def.38">FUNCTOR0:def 38</a></span>;<br/>
<a NAME="E2:26_1_1"/><span class="lab"><font color="Green" title="E32">A21</font></span>: 
(  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c19">MG</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> <font color="Maroon" title="c12">OGI</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c15">OFI</font></span>)</span> <a href="pboole.html#K8" title="PBOOLE:func.8">**</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">MF</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> <font color="Maroon" title="c15">OFI</font></span>)</span></span>)</span> <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="c3">C</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C</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="txt" href="#E1:26"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="functor0.html#D38" title="FUNCTOR0:def.38">FUNCTOR0:def 38</a>, <a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E3:26_1_1"/><span class="lab"><font color="Green" title="E33">A22</font></span>: 
<font color="Maroon" title="c17">OG</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">OG</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="txt" href="#E27:26"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="txt" href="#E4:26_1"><span class="lab"><font color="Green" title="E30">A19</font></span></a>, <a class="ref" href="funct_2.html#T29" title="FUNCT_2:th.29">FUNCT_2:29</a></span>;<br/>
<span class="lab"><font color="Green" title="E34">A23</font></span>: <font color="Maroon" title="c18">OFG</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</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">F</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c17">OG</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D36" title="FUNCTOR0:def.36">FUNCTOR0:def 36</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c17">OG</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</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="c5">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="#E19:26"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E27:26"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="ref" href="funct_1.html#T44" title="FUNCT_1:th.44">FUNCT_1:44</a></span>
;<br/>
<span class="kw">let </span><font color="Maroon" title="c21">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c20">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="p2">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <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="c5">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span></span>)</span> <a href="pboole.html#K8" title="PBOOLE:func.8">**</a>  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c5">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> <font color="Maroon" title="c21">i</font> )</span><br/>

<span class="kw">assume </span><a NAME="E5:26_1_1"/><span class="lab"><font color="Green" title="E35">A24</font></span>: 
<font color="Maroon" title="c21">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c20">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="p2">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <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="c5">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span></span>)</span> <a href="pboole.html#K8" title="PBOOLE:func.8">**</a>  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c5">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> <font color="Maroon" title="c21">i</font></span><br/>

<span class="lab"><font color="Green" title="E36">A25</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">MF</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">OG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c17">OG</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p0">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">MG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c18">OFG</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">MF</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">OG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">OGI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c15">OFI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">MG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c18">OFG</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></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="#E5:26_1_1"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="ref" href="funct_2.html#T15" title="FUNCT_2:th.15">FUNCT_2:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">MF</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c17">OG</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c12">OGI</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c15">OFI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">MG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c18">OFG</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></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="#E5:26_1_1"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="ref" href="funct_2.html#T5" title="FUNCT_2:th.5">FUNCT_2:5</a>, <a class="ref" href="funct_2.html#T15" title="FUNCT_2:th.15">FUNCT_2:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">MF</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p0"><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>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c15">OFI</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">MG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c18">OFG</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></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="#E5:26_1_1"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="txt" href="#E3:26_1_1"><span class="lab"><font color="Green" title="E33">A22</font></span></a>, <a class="ref" href="funct_2.html#T15" title="FUNCT_2:th.15">FUNCT_2:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">MF</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">MG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c12">OGI</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c15">OFI</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></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="#E4:26_1_1"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="ref" href="funct_2.html#T17" title="FUNCT_2:th.17">FUNCT_2:17</a></span>
;<br/>
<a NAME="E7:26_1_1"/>
<font color="Maroon" title="c18">OFG</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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="c3">C</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<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="txt" href="#E28:26"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="ref" href="functor1.html#T2" target="_self" title="FUNCTOR1:th.2">Th3</a>, <a class="ref" href="functor1.html#T5" target="_self" title="FUNCTOR1:th.5">Th6</a></span>;<br/>
<a NAME="E8:26_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A26</font></span>: 
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">MF</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c17">OG</font></span>)</span> <a href="pboole.html#K8" title="PBOOLE:func.8">**</a> <font color="Maroon" title="c19">MG</font></span>)</span> <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> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c18">OFG</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#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="txt" href="#E5:26_1_1"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="ref" href="funct_2.html#T5" title="FUNCT_2:th.5">FUNCT_2:5</a>, <a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E9:26_1_1"/><span class="lab"><font color="Green" title="E38">A27</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="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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="c3">C</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<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="txt" href="#E28:26"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="ref" href="functor1.html#T2" target="_self" title="FUNCTOR1:th.2">Th3</a>, <a class="ref" href="functor1.html#T5" target="_self" title="FUNCTOR1:th.5">Th6</a></span>;<br/>
<a NAME="E10:26_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A28</font></span>: 
<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="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#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="txt" href="#E5:26_1_1"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="ref" href="funct_2.html#T5" title="FUNCT_2:th.5">FUNCT_2:5</a></span>;<br/>
<a NAME="E11:26_1_1"/>
<font color="Maroon" title="c21">i</font> <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"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <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="#E5:26_1_1"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="txt" href="#E9:26_1_1"><span class="lab"><font color="Green" title="E38">A27</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="E40">A29</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c20">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="p2">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">MFG</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">(<span class="default"><span class="p2">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26_1"><span class="lab"><font color="Green" title="E28">A17</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="c16">MFG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p4">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</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="#E31:26"><span class="lab"><font color="Green" title="E25">A14</font></span></a>, <a class="txt" href="#E32:26"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="txt" href="#E10:26_1_1"><span class="lab"><font color="Green" title="E39">A28</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="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">MF</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c17">OG</font></span>)</span> <a href="pboole.html#K8" title="PBOOLE:func.8">**</a> <font color="Maroon" title="c19">MG</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c18">OFG</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</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="ref" href="functor0.html#D36" title="FUNCTOR0:def.36">FUNCTOR0:def 36</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">MF</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c17">OG</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c18">OFG</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">MG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c18">OFG</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></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="#E8:26_1_1"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="ref" href="pboole.html#D19" title="PBOOLE:def.19">PBOOLE:def 19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">MF</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">OG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c17">OG</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p0">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">MG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c18">OFG</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></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="#E5:26_1_1"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="txt" href="#E9:26_1_1"><span class="lab"><font color="Green" title="E38">A27</font></span></a>, <a class="txt" href="#E4:26_1_1"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="ref" href="funct_2.html#T5" title="FUNCT_2:th.5">FUNCT_2:5</a>, <a class="ref" href="funct_2.html#T15" title="FUNCT_2:th.15">FUNCT_2:15</a></span>
;<br/>
<a NAME="E13:26_1_1"/><span class="lab"><font color="Green" title="E41">A30</font></span>: 
<font color="Maroon" title="c15">OFI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#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="txt" href="#E5:26_1_1"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="ref" href="funct_2.html#T5" title="FUNCT_2:th.5">FUNCT_2:5</a></span>;<br/>
<a NAME="E14:26_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A31</font></span>: 
<font color="Maroon" title="c8">MF</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">OFI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</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="#E6:26"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="ref" href="msualg_3.html#T1" title="MSUALG_3:th.1">MSUALG_3:1</a></span>;<br/>
<a NAME="E15:26_1_1"/><span class="lab"><font color="Green" title="E43">A32</font></span>: 
<font color="Maroon" title="c12">OGI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">OFI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</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="txt" href="#E13:26_1_1"><span class="lab"><font color="Green" title="E41">A30</font></span></a>, <a class="ref" href="funct_2.html#T5" title="FUNCT_2:th.5">FUNCT_2:5</a></span>;<br/>
<a NAME="E16:26_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A33</font></span>: 
<font color="Maroon" title="c19">MG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">OGI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c15">OFI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></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="#E13:26"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="ref" href="msualg_3.html#T1" title="MSUALG_3:th.1">MSUALG_3:1</a></span>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">MF</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">MG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c12">OGI</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c15">OFI</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">MF</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">MG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">OGI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c15">OFI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span></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="#E5:26_1_1"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="ref" href="funct_2.html#T15" title="FUNCT_2:th.15">FUNCT_2:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">MG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">OGI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c15">OFI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">MF</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c15">OFI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span> <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="#E16:26_1_1"><span class="lab"><font color="Green" title="E44">A33</font></span></a>, <a class="txt" href="#E14:26_1_1"><span class="lab"><font color="Green" title="E42">A31</font></span></a>, <a class="ref" href="funct_1.html#T44" title="FUNCT_1:th.44">FUNCT_1:44</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">MG</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="p2">(<span class="default"><font color="Maroon" title="c12">OGI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c15">OFI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">MF</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span> <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="#E24:26"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="txt" href="#E13:26"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E15:26_1_1"><span class="lab"><font color="Green" title="E43">A32</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="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c19">MG</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> <font color="Maroon" title="c12">OGI</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="c15">OFI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">MF</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span> <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="#E5:26_1_1"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="ref" href="funct_2.html#T5" title="FUNCT_2:th.5">FUNCT_2:5</a>, <a class="ref" href="funct_2.html#T15" title="FUNCT_2:th.15">FUNCT_2:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c19">MG</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> <font color="Maroon" title="c12">OGI</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c15">OFI</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">MF</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c15">OFI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span> <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="#E5:26_1_1"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="ref" href="funct_2.html#T15" title="FUNCT_2:th.15">FUNCT_2:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c19">MG</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> <font color="Maroon" title="c12">OGI</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c15">OFI</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">MF</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="p2">(<span class="default"><font color="Maroon" title="c15">OFI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:26"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E16:26"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E13:26_1_1"><span class="lab"><font color="Green" title="E41">A30</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="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c19">MG</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> <font color="Maroon" title="c12">OGI</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c15">OFI</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">MF</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> <font color="Maroon" title="c15">OFI</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:26_1_1"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="ref" href="funct_2.html#T15" title="FUNCT_2:th.15">FUNCT_2:15</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E18:26_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c20">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="p2">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <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="c5">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span></span>)</span> <a href="pboole.html#K8" title="PBOOLE:func.8">**</a>  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c5">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> <font color="Maroon" title="c21">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26_1_1"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="txt" href="#E5:26_1_1"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="txt" href="#E2:26_1_1"><span class="lab"><font color="Green" title="E32">A21</font></span></a>, <a class="txt" href="#E12:26_1_1"><span class="lab"><font color="Green" title="E40">A29</font></span></a>, <a class="txt" href="#E6:26_1_1"><span class="lab"><font color="Green" title="E36">A25</font></span></a>, <a class="ref" href="pboole.html#D19" title="PBOOLE:def.19">PBOOLE:def 19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> = 
<span class="p1">(<span class="default"> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c6">GI</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="c7">FI</font></span>)</span> <a href="pboole.html#K8" title="PBOOLE:func.8">**</a>  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c7">FI</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E4:26"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E3:26_1"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="ref" href="pboole.html#T3" title="PBOOLE:th.3">PBOOLE:3</a></span>
<br/>.= 
 the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c6">GI</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c7">FI</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D36" title="FUNCTOR0:def.36">FUNCTOR0:def 36</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E7:26_1"/>
 the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c6">GI</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c7">FI</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a></span>)</span> = 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></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="#E28:26"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="ref" href="functor0.html#D38" title="FUNCTOR0:def.38">FUNCTOR0:def 38</a></span>
<br/>.= 
<span class="p1">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">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="c4">G</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D36" title="FUNCTOR0:def.36">FUNCTOR0:def 36</a></span>
<br/>.= 
<span class="p1">(<span class="default"> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</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="c5">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="#E19:26"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E27:26"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="ref" href="funct_1.html#T44" title="FUNCT_1:th.44">FUNCT_1:44</a></span>
<br/>.= 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c6">GI</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="c5">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="#E2:26"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="ref" href="functor0.html#D38" title="FUNCTOR0:def.38">FUNCTOR0:def 38</a></span>
<br/>.= 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c6">GI</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="c7">FI</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E4:26"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="ref" href="functor0.html#D38" title="FUNCTOR0:def.38">FUNCTOR0:def 38</a></span>
<br/>.= 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c6">GI</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c7">FI</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D36" title="FUNCTOR0:def.36">FUNCTOR0:def 36</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E35:26"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">GI</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c7">FI</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:26"><span class="lab"><font color="Green" title="E27">A16</font></span></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>
