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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">F</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>  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/>



<span class="kw">assume </span><a NAME="E1:66"/><span class="lab"><font color="Green" title="E35">A1</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<a NAME="E2:66"/>
<font color="Maroon" title="c3">F</font> is  <a href="functor0.html#V20" title="FUNCTOR0:attr.20">surjective</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:66"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="functor0.html#D36" title="FUNCTOR0:def.36">FUNCTOR0:def 36</a></span>;<br/>
<a NAME="E3:66"/><span class="kw">then </span>
<font color="Maroon" title="c3">F</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#D35" title="FUNCTOR0:def.35">FUNCTOR0:def 35</a></span>;<br/>
<a NAME="E4:66"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A2</font></span>: 
<font color="Maroon" title="c3">F</font> is  <a href="functor0.html#V7" title="FUNCTOR0:attr.7">coreflexive</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#T48" title="FUNCTOR0:th.48">FUNCTOR0:48</a></span>;<br/>
<a NAME="E5:66"/>
 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>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:66"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="functor0.html#T50" title="FUNCTOR0:th.50">FUNCTOR0:50</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">F9</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/>
<span class="kw">let </span><font color="Maroon" title="c5">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c5">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="c5">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/><span class="kw">let </span><font color="Maroon" title="c6">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c6">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="c6">B2</font>,<font color="Maroon" title="c5">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/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E7:66"/>
<font color="Maroon" title="c5">B1</font> is   <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c1">A1</font>
 <span class="kw">and </span><br/><a NAME="E8:66"/>
<font color="Maroon" title="c6">B2</font> is   <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c2">A2</font>
 ; <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c5">B1</font>,<font color="Maroon" title="c6">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">a9</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c5">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">a9</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">a9</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">b9</font>, <font color="Olive" title="b3">c9</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c5">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">b9</font>,<font color="Olive" title="b3">c9</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">b9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b</font> &amp; <font color="Olive" title="b3">c9</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">f9</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b2">b9</font>,<font color="Olive" title="b3">c9</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">f9</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">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <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="c6">B2</font>,<font color="Maroon" title="c5">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/>

<span class="kw">given </span><font color="Maroon" title="c7">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">B1</font>,<font color="Maroon" title="c6">B2</font><span class="kw"> such that </span><a NAME="E10:66"/><span class="lab"><font color="Green" title="E37">A3</font></span>: 
<font color="Maroon" title="c7">G</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> 
 <span class="kw">and </span><br/><a NAME="E11:66"/><span class="lab"><font color="Green" title="E38">A4</font></span>: 
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">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="c7">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>
 <span class="kw">and </span><br/><a NAME="E12:66"/><span class="lab"><font color="Green" title="E39">A5</font></span>: 
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">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="c7">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">B2</font>,<font color="Maroon" title="c5">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/>

<a NAME="E13:66"/>
<font color="Maroon" title="c7">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="#E10:66"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="ref" href="functor0.html#D36" title="FUNCTOR0:def.36">FUNCTOR0:def 36</a></span>;<br/>
<a NAME="E14:66"/><span class="kw">then </span>
<font color="Maroon" title="c7">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#D35" title="FUNCTOR0:def.35">FUNCTOR0:def 35</a></span>;<br/>
<a NAME="E15:66"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A6</font></span>: 
<font color="Maroon" title="c7">G</font> is  <a href="functor0.html#V7" title="FUNCTOR0:attr.7">coreflexive</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#T48" title="FUNCTOR0:th.48">FUNCTOR0:48</a></span>;<br/>
<span class="kw">thus </span><a NAME="E16:66"/>
( <font color="Maroon" title="c6">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="c5">B1</font> is   <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c1">A1</font> )
 ; <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c6">B2</font>,<font color="Maroon" title="c5">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">a9</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c6">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">a9</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">a9</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">b9</font>, <font color="Olive" title="b3">c9</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c6">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">b9</font>,<font color="Olive" title="b3">c9</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">b9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b</font> &amp; <font color="Olive" title="b3">c9</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">f9</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b2">b9</font>,<font color="Olive" title="b3">c9</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">f9</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">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span>,<font color="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/>

<span class="kw">consider </span><font color="Maroon" title="c8">H</font> being    <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c6">B2</font>,<font color="Maroon" title="c5">B1</font><span class="kw"> such that </span><br/><a NAME="E18:66"/><span class="lab"><font color="Green" title="E41">A7</font></span>: 
<font color="Maroon" title="c8">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">G</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> 
 <span class="kw">and </span><br/><a NAME="E19:66"/><span class="lab"><font color="Green" title="E42">A8</font></span>: 
( <font color="Maroon" title="c8">H</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>  &amp; <font color="Maroon" title="c8">H</font> is  <a href="functor0.html#V16" title="FUNCTOR0:attr.16">contravariant</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:66"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="ref" href="functor0.html#T50" title="FUNCTOR0:th.50">FUNCTOR0:50</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">H</font> = <font color="Maroon" title="c8">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="c6">B2</font>,<font color="Maroon" title="c5">B1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:66"><span class="lab"><font color="Green" title="E42">A8</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c9">H</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c9">H</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>  &amp; ( for <font color="Olive" title="b1">a9</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c6">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">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> holds <br/><font color="Maroon" title="c9">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b1">a9</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">b9</font>, <font color="Olive" title="b2">c9</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c6">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">b9</font>,<font color="Olive" title="b2">c9</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">b9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b2">c9</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">f9</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">b9</font>,<font color="Olive" title="b2">c9</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">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">f</font> holds <br/><font color="Maroon" title="c9">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Olive" title="b5">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span>,<font color="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/>

<span class="kw">thus </span><a NAME="E21:66"/>
<font color="Maroon" title="c9">H</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="#E19:66"><span class="lab"><font color="Green" title="E42">A8</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( for <font color="Olive" title="b1">a9</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c6">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">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> holds <br/><font color="Maroon" title="c9">H</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b1">a9</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">b9</font>, <font color="Olive" title="b2">c9</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c6">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">b9</font>,<font color="Olive" title="b2">c9</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">b9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b2">c9</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">f9</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">b9</font>,<font color="Olive" title="b2">c9</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">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">f</font> holds <br/><font color="Maroon" title="c9">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Olive" title="b5">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span>,<font color="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="E22:66"/><span class="lab"><font color="Green" title="E43">A9</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_2.html#D11" title="ALTCAT_2:def.11">ALTCAT_2:def 11</a></span>;<br/>
<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">b9</font>, <font color="Olive" title="b2">c9</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c6">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">b9</font>,<font color="Olive" title="b2">c9</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">b9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b2">c9</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">f9</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">b9</font>,<font color="Olive" title="b2">c9</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">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">f</font> holds <br/><font color="Maroon" title="c9">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Olive" title="b5">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span>,<font color="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"><span class="kw">let </span><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="c6">B2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c9">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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c9">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="c9">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="c5">B1</font>
 ;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c12">Ha</font> = <font color="Maroon" title="c9">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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:66"><span class="lab"><font color="Green" title="E43">A9</font></span></a></span>;<br/><a NAME="E3:66_1"/>
<font color="Maroon" title="c7">G</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:66"><span class="lab"><font color="Green" title="E38">A4</font></span></a></span>;<br/><a NAME="E4:66_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A11</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:66"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="txt" href="#E18:66"><span class="lab"><font color="Green" title="E41">A7</font></span></a>, <a class="txt" href="#E15:66"><span class="lab"><font color="Green" title="E40">A6</font></span></a>, <a class="ref" href="yellow20.html#T1" target="_self" title="YELLOW20:th.1">Th1</a></span>;<br/><span class="kw">assume </span><a NAME="E5:66_1"/>
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c9">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/><span class="kw">hence </span><a NAME="E6:66_1"/>
<font color="Maroon" title="c9">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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:66"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="txt" href="#E4:66"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="txt" href="#E4:66_1"><span class="lab"><font color="Green" title="E45">A11</font></span></a>, <a class="ref" href="yellow20.html#T1" target="_self" title="YELLOW20:th.1">Th1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">let </span><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="c6">B2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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">f9</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">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">f</font> holds <br/><font color="Maroon" title="c9">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Olive" title="b3">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span>,<font color="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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="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">f9</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">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> holds <br/><font color="Maroon" title="c9">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Olive" title="b1">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span>,<font color="Maroon" title="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/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E24:66"/><span class="lab"><font color="Green" title="E45">A12</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="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> 
 <span class="kw">and </span><br/><a NAME="E25:66"/><span class="lab"><font color="Green" title="E46">A13</font></span>: 
( <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f9</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">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> holds <br/><font color="Maroon" title="c9">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Olive" title="b1">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span>,<font color="Maroon" title="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/>

<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="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="c9">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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c9">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/>



<span class="kw">assume </span><a NAME="E26:66"/><span class="lab"><font color="Green" title="E47">A14</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c9">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="E27:66"/><span class="lab"><font color="Green" title="E48">A15</font></span>: 
( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="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> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:66"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="txt" href="#E25:66"><span class="lab"><font color="Green" title="E46">A13</font></span></a>, <a class="ref" href="altcat_2.html#T32" title="ALTCAT_2:th.32">ALTCAT_2:32</a></span>;<br/>
<a NAME="E28:66"/><span class="lab"><font color="Green" title="E49">A16</font></span>: 
( <font color="Maroon" title="c7">G</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">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="c7">G</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">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> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:66"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="txt" href="#E18:66"><span class="lab"><font color="Green" title="E41">A7</font></span></a>, <a class="txt" href="#E15:66"><span class="lab"><font color="Green" title="E40">A6</font></span></a>, <a class="ref" href="yellow20.html#T1" target="_self" title="YELLOW20:th.1">Th1</a></span>;<br/>
<a NAME="E29:66"/><span class="lab"><font color="Green" title="E50">A17</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">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="c9">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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:66"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="ref" href="functor0.html#D20" title="FUNCTOR0:def.20">FUNCTOR0:def 20</a></span>;<br/>
<a NAME="E30:66"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A18</font></span>: 
<font color="Maroon" title="c9">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="c9">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="c9">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>
 
;<br/>
<a NAME="E31:66"/><span class="lab"><font color="Green" title="E52">A19</font></span>: 
( <font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> </span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="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> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:66"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="txt" href="#E4:66"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="ref" href="yellow20.html#T1" target="_self" title="YELLOW20:th.1">Th1</a></span>;<br/>
<a NAME="E32:66"/><span class="lab"><font color="Green" title="E53">A20</font></span>: 
( <font color="Maroon" title="c9">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="c9">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> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:66"><span class="lab"><font color="Green" title="E44">A10</font></span></a>, <a class="txt" href="#E25:66"><span class="lab"><font color="Green" title="E46">A13</font></span></a></span>;<br/>
<a NAME="E33:66"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A21</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">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="c9">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_2.html#T32" title="ALTCAT_2:th.32">ALTCAT_2:32</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c16">Hf</font> = <font color="Maroon" title="c9">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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:66"><span class="lab"><font color="Green" title="E51">A18</font></span></a></span>;<br/>
<font color="Maroon" title="c7">G</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:66"><span class="lab"><font color="Green" title="E39">A5</font></span></a>, <a class="txt" href="#E32:66"><span class="lab"><font color="Green" title="E53">A20</font></span></a>, <a class="txt" href="#E29:66"><span class="lab"><font color="Green" title="E50">A17</font></span></a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:66"><span class="lab"><font color="Green" title="E54">A21</font></span></a>, <a class="txt" href="#E30:66"><span class="lab"><font color="Green" title="E51">A18</font></span></a>, <a class="txt" href="#E27:66"><span class="lab"><font color="Green" title="E48">A15</font></span></a>, <a class="txt" href="#E31:66"><span class="lab"><font color="Green" title="E52">A19</font></span></a>, <a class="ref" href="functor0.html#D17" title="FUNCTOR0:def.17">FUNCTOR0:def 17</a></span>
;<br/>
<a NAME="E36:66"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:66"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="txt" href="#E18:66"><span class="lab"><font color="Green" title="E41">A7</font></span></a>, <a class="txt" href="#E29:66"><span class="lab"><font color="Green" title="E50">A17</font></span></a>, <a class="txt" href="#E28:66"><span class="lab"><font color="Green" title="E49">A16</font></span></a>, <a class="ref" href="yellow20.html#T3" target="_self" title="YELLOW20:th.3">Th3</a></span>;<br/>
<span class="kw">hence </span><font color="Maroon" title="c9">H</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Maroon" title="c14">f</font> = 
<font color="Maroon" title="c4">F9</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Maroon" title="c15">f1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:66"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="txt" href="#E26:66"><span class="lab"><font color="Green" title="E47">A14</font></span></a>, <a class="txt" href="#E33:66"><span class="lab"><font color="Green" title="E54">A21</font></span></a>, <a class="txt" href="#E30:66"><span class="lab"><font color="Green" title="E51">A18</font></span></a>, <a class="txt" href="#E31:66"><span class="lab"><font color="Green" title="E52">A19</font></span></a>, <a class="ref" href="yellow20.html#T3" target="_self" title="YELLOW20:th.3">Th3</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:66"><span class="lab"><font color="Green" title="E54">A21</font></span></a>, <a class="txt" href="#E30:66"><span class="lab"><font color="Green" title="E51">A18</font></span></a>, <a class="txt" href="#E27:66"><span class="lab"><font color="Green" title="E48">A15</font></span></a>, <a class="ref" href="functor0.html#D17" title="FUNCTOR0:def.17">FUNCTOR0:def 17</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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