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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</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#V15" title="FUNCTOR0:attr.15">covariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>  st <font color="Olive" title="b1">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> holds <br/><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> <a href="yellow20.html#R2" title="YELLOW20:pred.2">are_isomorphic_under</a> <font color="Olive" title="b1">F</font></span><br/><b>let </b><font color="Maroon" title="c3">F</font> be  <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</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 <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> <a href="yellow20.html#R2" title="YELLOW20:pred.2">are_isomorphic_under</a> <font color="Maroon" title="c3">F</font> )</span><br/>



<b>assume </b><a NAME="E1:54"/><i><font color="Green" title="E32">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"> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> <a href="yellow20.html#R2" title="YELLOW20:pred.2">are_isomorphic_under</a> <font color="Maroon" title="c3">F</font></span><br/>

<a NAME="E2:54"/>
( <font color="Maroon" title="c1">A</font> is    <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c1">A</font> &amp; <font color="Maroon" title="c2">B</font> is    <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c2">B</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font> &amp; the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font> &amp; the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">B</font> )
 
<b>by </b><i><a class="ref" href="altcat_2.html#T21" title="ALTCAT_2:th.21">ALTCAT_2:21</a></i>;<br/>
<b>hence </b><a NAME="E3:54"/>
( <font color="Maroon" title="c1">A</font> is   <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c1">A</font> &amp; <font color="Maroon" title="c2">B</font> is   <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c2">B</font> )
 <b>by </b><i><a class="ref" href="altcat_4.html#T35" title="ALTCAT_4:th.35">ALTCAT_4:35</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow20.html#D4" target="_self" title="YELLOW20:def.4">YELLOW20:def 4</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#V15" title="FUNCTOR0:attr.15">covariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</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>, <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">A</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> <font color="Maroon" title="c3">F</font> <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>, <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">A</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#K6" title="FUNCTOR0:func.6">.</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> ) )</span><br/>

<b>take </b>
<font color="Maroon" title="c3">F</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> &amp; ( for <font color="Olive" title="b1">a'</font>, <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="c1">A</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="c3">F</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">a</font> ) &amp; ( for <font color="Olive" title="b1">b'</font>, <font color="Olive" title="b2">c'</font>, <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="c1">A</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="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</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> <font color="Maroon" title="c3">F</font>,<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="E4:54"/>
( <font color="Maroon" title="c3">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> &amp; ( for <font color="Olive" title="b1">a'</font>, <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="c1">A</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="c3">F</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">a</font> ) )
 <b>by </b><i><a class="txt" href="yellow20.html#E1:54"><i><font color="Green" title="E32">A1</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">b'</font>, <font color="Olive" title="b2">c'</font>, <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="c1">A</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="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</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> <font color="Maroon" title="c3">F</font>,<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>let </b><font color="Maroon" title="c4">b'</font>, <font color="Maroon" title="c5">c'</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</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="c1">A</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="c4">b'</font>,<font color="Maroon" title="c5">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="c4">b'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> &amp; <font color="Maroon" title="c5">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="c4">b'</font>,<font color="Maroon" title="c5">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="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</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> <font color="Maroon" title="c3">F</font>,<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="c6">b</font>, <font color="Maroon" title="c7">c</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</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="c4">b'</font>,<font color="Maroon" title="c5">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="c4">b'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b</font> &amp; <font color="Maroon" title="c5">c'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c</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="c4">b'</font>,<font color="Maroon" title="c5">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="c6">b</font>,<font color="Maroon" title="c7">c</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="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</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> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c7">c</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="E5:54"/><i><font color="Green" title="E33">A2</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="c4">b'</font>,<font color="Maroon" title="c5">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="c4">b'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b</font> &amp; <font color="Maroon" title="c5">c'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">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="c4">b'</font>,<font color="Maroon" title="c5">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="c6">b</font>,<font color="Maroon" title="c7">c</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="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</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> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c7">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">f</font></span><br/>

<a NAME="E6:54"/><b>then </b>
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c6">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c7">c</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="ref" href="functor0.html#D19" title="FUNCTOR0:def.19">FUNCTOR0:def 19</a></i>;<br/>
<b>hence </b><a NAME="E7:54"/>
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="c4">b'</font>,<font color="Maroon" title="c5">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="c6">b</font>,<font color="Maroon" title="c7">c</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="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</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> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c7">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">f</font>
 <b>by </b><i><a class="txt" href="yellow20.html#E5:54"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="functor0.html#D16" title="FUNCTOR0:def.16">FUNCTOR0:def 16</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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