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<b>let </b><font color="Maroon" title="c1">A1</font>, <font color="Maroon" title="c2">A2</font> be   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">F</font> being <a href="functor0.html#V16" title="FUNCTOR0:attr.16">contravariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c1">A1</font>,<font color="Maroon" title="c2">A2</font>  st <font color="Olive" title="b1">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> holds <br/>for <font color="Olive" title="b2">B1</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c1">A1</font><br/> for <font color="Olive" title="b3">B2</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c2">A2</font>  st <font color="Olive" title="b2">B1</font>,<font color="Olive" title="b3">B2</font> <a href="yellow20.html#R3" title="YELLOW20:pred.3">are_anti-isomorphic_under</a> <font color="Olive" title="b1">F</font> holds <br/><font color="Olive" title="b3">B2</font>,<font color="Olive" title="b2">B1</font> <a href="yellow20.html#R3" title="YELLOW20:pred.3">are_anti-isomorphic_under</a> <font color="Olive" title="b1">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span><br/><b>let </b><font color="Maroon" title="c3">F</font> be  <a href="functor0.html#V16" title="FUNCTOR0:attr.16">contravariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c1">A1</font>,<font color="Maroon" title="c2">A2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> implies for <font color="Olive" title="b1">B1</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c1">A1</font><br/> for <font color="Olive" title="b2">B2</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c2">A2</font>  st <font color="Olive" title="b1">B1</font>,<font color="Olive" title="b2">B2</font> <a href="yellow20.html#R3" title="YELLOW20:pred.3">are_anti-isomorphic_under</a> <font color="Maroon" title="c3">F</font> holds <br/><font color="Olive" title="b2">B2</font>,<font color="Olive" title="b1">B1</font> <a href="yellow20.html#R3" title="YELLOW20:pred.3">are_anti-isomorphic_under</a> <font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  )</span><br/>



<b>assume </b><a NAME="E1:66"/><i><font color="Green" title="E36">A1</font></i>: 
<font color="Maroon" title="c3">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">B1</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c1">A1</font><br/> for <font color="Olive" title="b2">B2</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c2">A2</font>  st <font color="Olive" title="b1">B1</font>,<font color="Olive" title="b2">B2</font> <a href="yellow20.html#R3" title="YELLOW20:pred.3">are_anti-isomorphic_under</a> <font color="Maroon" title="c3">F</font> holds <br/><font color="Olive" title="b2">B2</font>,<font color="Olive" title="b1">B1</font> <a href="yellow20.html#R3" title="YELLOW20:pred.3">are_anti-isomorphic_under</a> <font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span><br/>

<b>let </b><font color="Maroon" title="c4">B1</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c1">A1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">B2</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c2">A2</font>  st <font color="Maroon" title="c4">B1</font>,<font color="Olive" title="b1">B2</font> <a href="yellow20.html#R3" title="YELLOW20:pred.3">are_anti-isomorphic_under</a> <font color="Maroon" title="c3">F</font> holds <br/><font color="Olive" title="b1">B2</font>,<font color="Maroon" title="c4">B1</font> <a href="yellow20.html#R3" title="YELLOW20:pred.3">are_anti-isomorphic_under</a> <font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span><br/><b>let </b><font color="Maroon" title="c5">B2</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c2">A2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">B1</font>,<font color="Maroon" title="c5">B2</font> <a href="yellow20.html#R3" title="YELLOW20:pred.3">are_anti-isomorphic_under</a> <font color="Maroon" title="c3">F</font> implies <font color="Maroon" title="c5">B2</font>,<font color="Maroon" title="c4">B1</font> <a href="yellow20.html#R3" title="YELLOW20:pred.3">are_anti-isomorphic_under</a> <font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  )</span><br/>



<b>assume </b><a NAME="E2:66"/>
( <font color="Maroon" title="c4">B1</font> is   <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c1">A1</font> &amp; <font color="Maroon" title="c5">B2</font> is   <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c2">A2</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow20.html#D5" target="_self" title="YELLOW20:def.5">YELLOW20:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( for <font color="Olive" title="b1">G</font> being <a href="functor0.html#V16" title="FUNCTOR0:attr.16">contravariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c4">B1</font>,<font color="Maroon" title="c5">B2</font>  holds <br/>(  not <font color="Olive" title="b1">G</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> or  ex <font color="Olive" title="b2">a'</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c4">B1</font> ex <font color="Olive" title="b3">a</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A1</font> st <br/>( <font color="Olive" title="b2">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a</font> &amp; not <font color="Olive" title="b1">G</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b2">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b3">a</font> ) or  ex <font color="Olive" title="b2">b'</font>, <font color="Olive" title="b3">c'</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c4">B1</font> ex <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">c</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A1</font> st <br/>( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b2">b'</font>,<font color="Olive" title="b3">c'</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b2">b'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b</font> &amp; <font color="Olive" title="b3">c'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">c</font> &amp;  ex <font color="Olive" title="b6">f'</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b2">b'</font>,<font color="Olive" title="b3">c'</font> ex <font color="Olive" title="b7">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b4">b</font>,<font color="Olive" title="b5">c</font> st <br/>( <font color="Olive" title="b6">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">f</font> &amp; not <font color="Olive" title="b1">G</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Olive" title="b6">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <font color="Maroon" title="c3">F</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b5">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b7">f</font> ) ) ) or <font color="Maroon" title="c5">B2</font>,<font color="Maroon" title="c4">B1</font> <a href="yellow20.html#R3" title="YELLOW20:pred.3">are_anti-isomorphic_under</a> <font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  )</span><br/>

<b>given </b><font color="Maroon" title="c6">G</font> being  <a href="functor0.html#V16" title="FUNCTOR0:attr.16">contravariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c4">B1</font>,<font color="Maroon" title="c5">B2</font><b> such that </b><a NAME="E4:66"/><i><font color="Green" title="E37">A2</font></i>: 
<font color="Maroon" title="c6">G</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>
 <b>and </b><br/><a NAME="E5:66"/><i><font color="Green" title="E38">A3</font></i>: 
for <font color="Olive" title="b1">a</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c4">B1</font><br/> for <font color="Olive" title="b2">a1</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A1</font>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a1</font> holds <br/><font color="Maroon" title="c6">G</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b2">a1</font>
 <b>and </b><br/><a NAME="E6:66"/><i><font color="Green" title="E39">A4</font></i>: 
for <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">c</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c4">B1</font><br/> for <font color="Olive" title="b3">b1</font>, <font color="Olive" title="b4">c1</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A1</font>  st <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">c</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">b1</font> &amp; <font color="Olive" title="b2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">c1</font> holds <br/>for <font color="Olive" title="b5">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">c</font><br/> for <font color="Olive" title="b6">f1</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">c1</font>  st <font color="Olive" title="b5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">f1</font> holds <br/><font color="Maroon" title="c6">G</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Olive" title="b5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K7" title="FUNCTOR0:func.7">Morph-Map</a> <font color="Maroon" title="c3">F</font>,<font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">c1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">f1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">B2</font>,<font color="Maroon" title="c4">B1</font> <a href="yellow20.html#R3" title="YELLOW20:pred.3">are_anti-isomorphic_under</a> <font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span><br/>

<b>thus </b><a NAME="E7:66"/>
( <font color="Maroon" title="c5">B2</font> is   <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c2">A2</font> &amp; <font color="Maroon" title="c4">B1</font> is   <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c1">A1</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow20.html#D5" target="_self" title="YELLOW20:def.5">YELLOW20:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">G</font> being <a href="functor0.html#V16" title="FUNCTOR0:attr.16">contravariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c5">B2</font>,<font color="Maroon" title="c4">B1</font> st <br/>( <font color="Olive" title="b1">G</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> &amp; ( for <font color="Olive" title="b2">a'</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c5">B2</font><br/> for <font color="Olive" title="b3">a</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">A2</font>  st <font color="Olive" title="b2">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a</font> holds <br/><font color="Olive" title="b1">G</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b2">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b3">a</font> ) &amp; ( for <font color="Olive" title="b2">b'</font>, <font color="Olive" title="b3">c'</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c5">B2</font><br/> for <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">c</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">A2</font>  st <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b2">b'</font>,<font color="Olive" title="b3">c'</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b2">b'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b</font> &amp; <font color="Olive" title="b3">c'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">c</font> holds <br/>for <font color="Olive" title="b6">f'</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b2">b'</font>,<font color="Olive" title="b3">c'</font><br/> for <font color="Olive" title="b7">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b4">b</font>,<font color="Olive" title="b5">c</font>  st <font color="Olive" title="b6">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">f</font> holds <br/><font color="Olive" title="b1">G</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Olive" title="b6">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b5">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b7">f</font> ) )</span><br/>

<b>consider </b><font color="Maroon" title="c7">H</font> being    <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c5">B2</font>,<font color="Maroon" title="c4">B1</font><b> such that </b><br/><a NAME="E9:66"/><i><font color="Green" title="E40">A5</font></i>: 
( <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">G</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  &amp; <font color="Maroon" title="c7">H</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> &amp; <font color="Maroon" title="c7">H</font> is <a href="functor0.html#V16" title="FUNCTOR0:attr.16">contravariant</a> )
 <b>by </b><i><a class="txt" href="#E4:66"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="functor0.html#T50" title="FUNCTOR0:th.50">FUNCTOR0:50</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">H</font> = <font color="Maroon" title="c7">H</font> as  <a href="functor0.html#V16" title="FUNCTOR0:attr.16">contravariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c5">B2</font>,<font color="Maroon" title="c4">B1</font> <b>by </b><i><a class="txt" href="#E9:66"><i><font color="Green" title="E40">A5</font></i></a></i>;<br/>
<a NAME="E11:66"/>
 ex <font color="Olive" title="b1">H</font> being   <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c2">A2</font>,<font color="Maroon" title="c1">A1</font> st <br/>( <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  &amp; <font color="Olive" title="b1">H</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> &amp; <font color="Olive" title="b1">H</font> is <a href="functor0.html#V16" title="FUNCTOR0:attr.16">contravariant</a> )
 
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="functor0.html#T50" title="FUNCTOR0:th.50">FUNCTOR0:50</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c9">F'</font> = <font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  as  <a href="functor0.html#V16" title="FUNCTOR0:attr.16">contravariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c2">A2</font>,<font color="Maroon" title="c1">A1</font> ;<br/>
<b>take </b>
<font color="Maroon" title="c8">H</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">H</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> &amp; ( for <font color="Olive" title="b1">a'</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c5">B2</font><br/> for <font color="Olive" title="b2">a</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">A2</font>  st <font color="Olive" title="b1">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> holds <br/><font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b1">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b2">a</font> ) &amp; ( for <font color="Olive" title="b1">b'</font>, <font color="Olive" title="b2">c'</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c5">B2</font><br/> for <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">A2</font>  st <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b1">b'</font>,<font color="Olive" title="b2">c'</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b1">b'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b2">c'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">c</font> holds <br/>for <font color="Olive" title="b5">f'</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">b'</font>,<font color="Olive" title="b2">c'</font><br/> for <font color="Olive" title="b6">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font>  st <font color="Olive" title="b5">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">f</font> holds <br/><font color="Maroon" title="c8">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Olive" title="b5">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">f</font> ) )</span><br/>

<b>thus </b><a NAME="E13:66"/>
<font color="Maroon" title="c8">H</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>
 <b>by </b><i><a class="txt" href="#E9:66"><i><font color="Green" title="E40">A5</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">a'</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c5">B2</font><br/> for <font color="Olive" title="b2">a</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">A2</font>  st <font color="Olive" title="b1">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> holds <br/><font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b1">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b2">a</font> ) &amp; ( for <font color="Olive" title="b1">b'</font>, <font color="Olive" title="b2">c'</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c5">B2</font><br/> for <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">A2</font>  st <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b1">b'</font>,<font color="Olive" title="b2">c'</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b1">b'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b2">c'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">c</font> holds <br/>for <font color="Olive" title="b5">f'</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">b'</font>,<font color="Olive" title="b2">c'</font><br/> for <font color="Olive" title="b6">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font>  st <font color="Olive" title="b5">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">f</font> holds <br/><font color="Maroon" title="c8">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Olive" title="b5">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">f</font> ) )</span><br/>

<a NAME="E14:66"/><i><font color="Green" title="E41">A6</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">B1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A1</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">B2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">A2</font> )
 
<b>by </b><i><a class="ref" href="altcat_2.html#D11" title="ALTCAT_2:def.11">ALTCAT_2:def 11</a></i>;<br/>
<a NAME="E15:66"/>
( <font color="Maroon" title="c3">F</font> is <a href="functor0.html#V20" title="FUNCTOR0:attr.20">surjective</a> &amp; <font color="Maroon" title="c6">G</font> is <a href="functor0.html#V20" title="FUNCTOR0:attr.20">surjective</a> )
 
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="#E4:66"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="functor0.html#D36" title="FUNCTOR0:def.36">FUNCTOR0:def 36</a></i>;<br/>
<a NAME="E16:66"/><b>then </b>
( <font color="Maroon" title="c3">F</font> is <a href="functor0.html#V5" title="FUNCTOR0:attr.5">onto</a> &amp; <font color="Maroon" title="c6">G</font> is <a href="functor0.html#V5" title="FUNCTOR0:attr.5">onto</a> )
 
<b>by </b><i><a class="ref" href="functor0.html#D35" title="FUNCTOR0:def.35">FUNCTOR0:def 35</a></i>;<br/>
<a NAME="E17:66"/><b>then </b><i><font color="Green" title="E42">A7</font></i>: 
( <font color="Maroon" title="c3">F</font> is <a href="functor0.html#V7" title="FUNCTOR0:attr.7">coreflexive</a> &amp; <font color="Maroon" title="c6">G</font> is <a href="functor0.html#V7" title="FUNCTOR0:attr.7">coreflexive</a> )
 
<b>by </b><i><a class="ref" href="functor0.html#T48" title="FUNCTOR0:th.48">FUNCTOR0:48</a></i>;<br/>
<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">b'</font>, <font color="Olive" title="b2">c'</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c5">B2</font><br/> for <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">A2</font>  st <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b1">b'</font>,<font color="Olive" title="b2">c'</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b1">b'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b2">c'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">c</font> holds <br/>for <font color="Olive" title="b5">f'</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">b'</font>,<font color="Olive" title="b2">c'</font><br/> for <font color="Olive" title="b6">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font>  st <font color="Olive" title="b5">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">f</font> holds <br/><font color="Maroon" title="c8">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Olive" title="b5">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">f</font></span>
<div class="add"><b>let </b><font color="Maroon" title="c10">a</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c5">B2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a1</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">A2</font>  st <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a1</font> holds <br/><font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b1">a1</font></span><br/><b>let </b><font color="Maroon" title="c11">a1</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">A2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a1</font> implies <font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c11">a1</font> )</span><br/><a NAME="E1:66_1"/>
<font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">B1</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c12">Ha</font> = <font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c10">a</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A1</font> <b>by </b><i><a class="txt" href="#E14:66"><i><font color="Green" title="E41">A6</font></i></a></i>;<br/><b>assume </b><a NAME="E3:66_1"/><i><font color="Green" title="E44">A9</font></i>: 
<font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c11">a1</font></span><br/><a NAME="E4:66_1"/>
<font color="Maroon" title="c6">G</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c12">Ha</font>
 <b>by </b><i><a class="txt" href="#E5:66"><i><font color="Green" title="E38">A3</font></i></a></i>;<br/><a NAME="E5:66_1"/><b>then </b>
<font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c12">Ha</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">a</font>
 <b>by </b><i><a class="txt" href="#E4:66"><i><font color="Green" title="E37">A2</font></i></a>, <a class="txt" href="#E9:66"><i><font color="Green" title="E40">A5</font></i></a>, <a class="txt" href="#E17:66"><i><font color="Green" title="E42">A7</font></i></a>, <a class="ref" href="yellow20.html#T1" target="_self" title="YELLOW20:th.1">Th1</a></i>;<br/><b>hence </b><a NAME="E6:66_1"/>
<font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c11">a1</font>
 <b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="#E17:66"><i><font color="Green" title="E42">A7</font></i></a>, <a class="txt" href="#E3:66_1"><i><font color="Green" title="E44">A9</font></i></a>, <a class="ref" href="yellow20.html#T1" target="_self" title="YELLOW20:th.1">Th1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c10">b</font>, <font color="Maroon" title="c11">c</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c5">B2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">c</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">A2</font>  st <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c11">c</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c10">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">c</font> holds <br/>for <font color="Olive" title="b3">f'</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c11">c</font><br/> for <font color="Olive" title="b4">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">c</font>  st <font color="Olive" title="b3">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">f</font> holds <br/><font color="Maroon" title="c8">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Olive" title="b3">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span>,<font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">f</font></span><br/><b>let </b><font color="Maroon" title="c12">b1</font>, <font color="Maroon" title="c13">c1</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">A2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c11">c</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c10">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b1</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c1</font> implies for <font color="Olive" title="b1">f'</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c11">c</font><br/> for <font color="Olive" title="b2">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c12">b1</font>,<font color="Maroon" title="c13">c1</font>  st <font color="Olive" title="b1">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> holds <br/><font color="Maroon" title="c8">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Olive" title="b1">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span>,<font color="Maroon" title="c12">b1</font>,<font color="Maroon" title="c13">c1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">f</font> )</span><br/>



<b>assume </b><a NAME="E19:66"/><i><font color="Green" title="E44">A10</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c11">c</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c10">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b1</font> &amp; <font color="Maroon" title="c11">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f'</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c11">c</font><br/> for <font color="Olive" title="b2">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c12">b1</font>,<font color="Maroon" title="c13">c1</font>  st <font color="Olive" title="b1">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> holds <br/><font color="Maroon" title="c8">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Olive" title="b1">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span>,<font color="Maroon" title="c12">b1</font>,<font color="Maroon" title="c13">c1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">f</font></span><br/>

<b>let </b><font color="Maroon" title="c14">f</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c11">c</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c12">b1</font>,<font color="Maroon" title="c13">c1</font>  st <font color="Maroon" title="c14">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> holds <br/><font color="Maroon" title="c8">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Maroon" title="c14">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span>,<font color="Maroon" title="c12">b1</font>,<font color="Maroon" title="c13">c1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">f</font></span><br/><b>let </b><font color="Maroon" title="c15">f1</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c12">b1</font>,<font color="Maroon" title="c13">c1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c14">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">f1</font> implies <font color="Maroon" title="c8">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Maroon" title="c14">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span>,<font color="Maroon" title="c12">b1</font>,<font color="Maroon" title="c13">c1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">f1</font> )</span><br/>



<b>assume </b><a NAME="E20:66"/><i><font color="Green" title="E45">A11</font></i>: 
<font color="Maroon" title="c14">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">f1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Maroon" title="c14">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span>,<font color="Maroon" title="c12">b1</font>,<font color="Maroon" title="c13">c1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">f1</font></span><br/>

<a NAME="E21:66"/><i><font color="Green" title="E46">A12</font></i>: 
( <font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c10">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c12">b1</font> &amp; <font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c11">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c13">c1</font> &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c11">c</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c10">b</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<b>by </b><i><a class="txt" href="#E18:66"><i><font color="Green" title="E43">A8</font></i></a>, <a class="txt" href="#E19:66"><i><font color="Green" title="E44">A10</font></i></a>, <a class="ref" href="functor0.html#D20" title="FUNCTOR0:def.20">FUNCTOR0:def 20</a></i>;<br/>
<a NAME="E22:66"/><b>then </b><i><font color="Green" title="E47">A13</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c11">c</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c10">b</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c13">c1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c12">b1</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> &amp; <font color="Maroon" title="c8">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Maroon" title="c14">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c11">c</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c10">b</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> )
 
<b>by </b><i><a class="ref" href="altcat_2.html#T32" title="ALTCAT_2:th.32">ALTCAT_2:32</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c16">Hf</font> = <font color="Maroon" title="c8">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Maroon" title="c14">f</font> as   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c13">c1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c12">b1</font></span>)</span> ;<br/>
<a NAME="E24:66"/><i><font color="Green" title="E48">A14</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c11">c</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c12">b1</font>,<font color="Maroon" title="c13">c1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> &amp; <font color="Maroon" title="c14">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c10">b</font>,<font color="Maroon" title="c11">c</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> )
 
<b>by </b><i><a class="txt" href="#E19:66"><i><font color="Green" title="E44">A10</font></i></a>, <a class="ref" href="altcat_2.html#T32" title="ALTCAT_2:th.32">ALTCAT_2:32</a></i>;<br/>
<a NAME="E25:66"/><b>then </b><i><font color="Green" title="E49">A15</font></i>: 
( <font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c12">b1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b1</font> &amp; <font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c13">c1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">c1</font> &amp; <font color="Maroon" title="c14">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c12">b1</font>,<font color="Maroon" title="c13">c1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> )
 
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="#E17:66"><i><font color="Green" title="E42">A7</font></i></a>, <a class="ref" href="yellow20.html#T1" target="_self" title="YELLOW20:th.1">Th1</a></i>;<br/>
<a NAME="E26:66"/><i><font color="Green" title="E50">A16</font></i>: 
( <font color="Maroon" title="c6">G</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c10">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> &amp; <font color="Maroon" title="c6">G</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c11">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">c</font> )
 
<b>by </b><i><a class="txt" href="#E4:66"><i><font color="Green" title="E37">A2</font></i></a>, <a class="txt" href="#E9:66"><i><font color="Green" title="E40">A5</font></i></a>, <a class="txt" href="#E17:66"><i><font color="Green" title="E42">A7</font></i></a>, <a class="ref" href="yellow20.html#T1" target="_self" title="YELLOW20:th.1">Th1</a></i>;<br/>
<font color="Maroon" title="c6">G</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Maroon" title="c14">f</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="functor0.html#K7" title="FUNCTOR0:func.7">Morph-Map</a> <font color="Maroon" title="c3">F</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c13">c1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c12">b1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">Hf</font>
<b>by </b><i><a class="txt" href="#E6:66"><i><font color="Green" title="E39">A4</font></i></a>, <a class="txt" href="#E21:66"><i><font color="Green" title="E46">A12</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">F</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Maroon" title="c16">Hf</font>
<b>by </b><i><a class="txt" href="#E22:66"><i><font color="Green" title="E47">A13</font></i></a>, <a class="txt" href="#E25:66"><i><font color="Green" title="E49">A15</font></i></a>, <a class="ref" href="functor0.html#D17" title="FUNCTOR0:def.17">FUNCTOR0:def 17</a></i>
;<br/>
<a NAME="E28:66"/><b>then </b>
<font color="Maroon" title="c3">F</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Maroon" title="c16">Hf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">f</font>
 
<b>by </b><i><a class="txt" href="#E4:66"><i><font color="Green" title="E37">A2</font></i></a>, <a class="txt" href="#E9:66"><i><font color="Green" title="E40">A5</font></i></a>, <a class="txt" href="#E21:66"><i><font color="Green" title="E46">A12</font></i></a>, <a class="txt" href="#E26:66"><i><font color="Green" title="E50">A16</font></i></a>, <a class="ref" href="yellow20.html#T3" target="_self" title="YELLOW20:th.3">Th3</a></i>;<br/>
<b>hence </b><font color="Maroon" title="c8">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Maroon" title="c14">f</font> = 
<font color="Maroon" title="c9">F'</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Maroon" title="c15">f1</font>
<b>by </b><i><a class="txt" href="#E1:66"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="#E20:66"><i><font color="Green" title="E45">A11</font></i></a>, <a class="txt" href="#E22:66"><i><font color="Green" title="E47">A13</font></i></a>, <a class="txt" href="#E25:66"><i><font color="Green" title="E49">A15</font></i></a>, <a class="ref" href="yellow20.html#T3" target="_self" title="YELLOW20:th.3">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span>,<font color="Maroon" title="c12">b1</font>,<font color="Maroon" title="c13">c1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">f1</font>
<b>by </b><i><a class="txt" href="#E22:66"><i><font color="Green" title="E47">A13</font></i></a>, <a class="txt" href="#E24:66"><i><font color="Green" title="E48">A14</font></i></a>, <a class="ref" href="functor0.html#D17" title="FUNCTOR0:def.17">FUNCTOR0:def 17</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
