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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_1.html#V2" title="ALTCAT_1:attr.2">transitive</a> <a href="altcat_1.html#V12" title="ALTCAT_1:attr.12">with_units</a>  <a href="altcat_1.html#L2" title="ALTCAT_1:struct.2">AltCatStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><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><br/> for <font color="Olive" title="b2">o1</font>, <font color="Olive" title="b3">o2</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b4">a</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b2">o1</font>,<font color="Olive" title="b3">o2</font>  st <font color="Olive" title="b1">F</font> is <a href="functor0.html#V18" title="FUNCTOR0:attr.18">full</a> &amp; <font color="Olive" title="b1">F</font> is <a href="functor0.html#V17" title="FUNCTOR0:attr.17">faithful</a> &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b2">o1</font>,<font color="Olive" title="b3">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b3">o2</font>,<font color="Olive" title="b2">o1</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">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Olive" title="b4">a</font> is <a href="altcat_3.html#V2" title="ALTCAT_3:attr.2">coretraction</a> holds <br/><font color="Olive" title="b4">a</font> is <a href="altcat_3.html#V2" title="ALTCAT_3:attr.2">coretraction</a></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"> for <font color="Olive" title="b1">o1</font>, <font color="Olive" title="b2">o2</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b3">a</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">o1</font>,<font color="Olive" title="b2">o2</font>  st <font color="Maroon" title="c3">F</font> is <a href="functor0.html#V18" title="FUNCTOR0:attr.18">full</a> &amp; <font color="Maroon" title="c3">F</font> is <a href="functor0.html#V17" title="FUNCTOR0:attr.17">faithful</a> &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b1">o1</font>,<font color="Olive" title="b2">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b2">o2</font>,<font color="Olive" title="b1">o1</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="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Olive" title="b3">a</font> is <a href="altcat_3.html#V2" title="ALTCAT_3:attr.2">coretraction</a> holds <br/><font color="Olive" title="b3">a</font> is <a href="altcat_3.html#V2" title="ALTCAT_3:attr.2">coretraction</a></span><br/><b>let </b><font color="Maroon" title="c4">o1</font>, <font color="Maroon" title="c5">o2</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">a</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c5">o2</font>  st <font color="Maroon" title="c3">F</font> is <a href="functor0.html#V18" title="FUNCTOR0:attr.18">full</a> &amp; <font color="Maroon" title="c3">F</font> is <a href="functor0.html#V17" title="FUNCTOR0:attr.17">faithful</a> &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c5">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">o2</font>,<font color="Maroon" title="c4">o1</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="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Olive" title="b1">a</font> is <a href="altcat_3.html#V2" title="ALTCAT_3:attr.2">coretraction</a> holds <br/><font color="Olive" title="b1">a</font> is <a href="altcat_3.html#V2" title="ALTCAT_3:attr.2">coretraction</a></span><br/><b>let </b><font color="Maroon" title="c6">a</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c5">o2</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#V18" title="FUNCTOR0:attr.18">full</a> &amp; <font color="Maroon" title="c3">F</font> is <a href="functor0.html#V17" title="FUNCTOR0:attr.17">faithful</a> &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c5">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">o2</font>,<font color="Maroon" title="c4">o1</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="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c6">a</font> is <a href="altcat_3.html#V2" title="ALTCAT_3:attr.2">coretraction</a> implies <font color="Maroon" title="c6">a</font> is <a href="altcat_3.html#V2" title="ALTCAT_3:attr.2">coretraction</a> )</span><br/>







<b>assume </b><b>that </b><br/><a NAME="E1:30"/><i><font color="Green" title="E18">A1</font></i>: 
( <font color="Maroon" title="c3">F</font> is <a href="functor0.html#V18" title="FUNCTOR0:attr.18">full</a> &amp; <font color="Maroon" title="c3">F</font> is <a href="functor0.html#V17" title="FUNCTOR0:attr.17">faithful</a> )
 <b>and </b><br/><a NAME="E2:30"/><i><font color="Green" title="E19">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">o1</font>,<font color="Maroon" title="c5">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>and </b><br/><a NAME="E3:30"/><i><font color="Green" title="E20">A3</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="c5">o2</font>,<font color="Maroon" title="c4">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c6">a</font> is <a href="altcat_3.html#V2" title="ALTCAT_3:attr.2">coretraction</a> or <font color="Maroon" title="c6">a</font> is <a href="altcat_3.html#V2" title="ALTCAT_3:attr.2">coretraction</a> )</span><br/>

<b>assume </b><a NAME="E4:30"/>
<font color="Maroon" title="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c6">a</font> is <a href="altcat_3.html#V2" title="ALTCAT_3:attr.2">coretraction</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">a</font> is <a href="altcat_3.html#V2" title="ALTCAT_3:attr.2">coretraction</a></span><br/>

<b>then consider </b><font color="Maroon" title="c7">b</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c5">o2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c4">o1</font></span>)</span><b> such that </b><br/><a NAME="E6:30"/><i><font color="Green" title="E21">A4</font></i>: 
<font color="Maroon" title="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c6">a</font> <a href="altcat_3.html#NR2" title="ALTCAT_3:NR.2">is_right_inverse_of</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="ref" href="altcat_3.html#D3" title="ALTCAT_3:def.3">ALTCAT_3:def 3</a></i>;<br/>
<a NAME="E7:30"/><i><font color="Green" title="E22">A5</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c4">o1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="altcat_4.html#E6:30"><i><font color="Green" title="E21">A4</font></i></a>, <a class="ref" href="altcat_3.html#D1" title="ALTCAT_3:def.1">ALTCAT_3:def 1</a></i>;<br/>
<a NAME="E8:30"/>
 <a href="functor0.html#K5" title="FUNCTOR0:func.5">Morph-Map</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c5">o2</font>,<font color="Maroon" title="c4">o1</font> is <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>
 
<b>by </b><i><a class="txt" href="altcat_4.html#E1:30"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="functor1.html#T18" title="FUNCTOR1:th.18">FUNCTOR1:18</a></i>;<br/>
<a NAME="E9:30"/><b>then </b><i><font color="Green" title="E23">A6</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="functor0.html#K5" title="FUNCTOR0:func.5">Morph-Map</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c5">o2</font>,<font color="Maroon" title="c4">o1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c5">o2</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="c4">o1</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="funct_2.html#D3" title="FUNCT_2:def.3">FUNCT_2:def 3</a></i>;<br/>
<a NAME="E10:30"/><i><font color="Green" title="E24">A7</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="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c5">o2</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="c4">o1</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="altcat_4.html#E3:30"><i><font color="Green" title="E20">A3</font></i></a>, <a class="ref" href="functor0.html#D19" title="FUNCTOR0:def.19">FUNCTOR0:def 19</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c8">a'</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E12:30"/><i><font color="Green" title="E25">A8</font></i>: 
<font color="Maroon" title="c8">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="functor0.html#K5" title="FUNCTOR0:func.5">Morph-Map</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c5">o2</font>,<font color="Maroon" title="c4">o1</font></span>)</span>
 <b>and </b><br/><a NAME="E13:30"/><i><font color="Green" title="E26">A9</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K5" title="FUNCTOR0:func.5">Morph-Map</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c5">o2</font>,<font color="Maroon" title="c4">o1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">a'</font>
 <b>by </b><i><a class="txt" href="altcat_4.html#E9:30"><i><font color="Green" title="E23">A6</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E14:30"/><i><font color="Green" title="E27">A10</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="functor0.html#K5" title="FUNCTOR0:func.5">Morph-Map</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c4">o1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c4">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">a'</font> = <font color="Maroon" title="c8">a'</font> as   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c5">o2</font>,<font color="Maroon" title="c4">o1</font> <b>by </b><i><a class="txt" href="altcat_4.html#E10:30"><i><font color="Green" title="E24">A7</font></i></a>, <a class="txt" href="altcat_4.html#E12:30"><i><font color="Green" title="E25">A8</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c9">a'</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_3.html#D3" title="ALTCAT_3:def.3">ALTCAT_3:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">a'</font> <a href="altcat_3.html#R1" title="ALTCAT_3:pred.1">is_left_inverse_of</a> <font color="Maroon" title="c6">a</font></span><br/>

<a NAME="E16:30"/><i><font color="Green" title="E28">A11</font></i>: 
 <a href="functor0.html#K5" title="FUNCTOR0:func.5">Morph-Map</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c4">o1</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="altcat_4.html#E1:30"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="functor1.html#T19" title="FUNCTOR1:th.19">FUNCTOR1:19</a></i>;<br/>
<span class="p1">(<span class="default"><a href="functor0.html#K5" title="FUNCTOR0:func.5">Morph-Map</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c4">o1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c4">o1</font></span>)</span> = 
<font color="Maroon" title="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c4">o1</font></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#D16" title="FUNCTOR0:def.16">FUNCTOR0:def 16</a></i>
<br/>.= 
 <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c4">o1</font></span>)</span>
<b>by </b><i><a class="ref" href="functor2.html#T2" title="FUNCTOR2:th.2">FUNCTOR2:2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c9">a'</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c6">a</font></span>)</span>
<b>by </b><i><a class="txt" href="altcat_4.html#E3:30"><i><font color="Green" title="E20">A3</font></i></a>, <a class="txt" href="altcat_4.html#E7:30"><i><font color="Green" title="E22">A5</font></i></a>, <a class="txt" href="altcat_4.html#E10:30"><i><font color="Green" title="E24">A7</font></i></a>, <a class="txt" href="altcat_4.html#E13:30"><i><font color="Green" title="E26">A9</font></i></a>, <a class="ref" href="functor0.html#D16" title="FUNCTOR0:def.16">FUNCTOR0:def 16</a></i>
<br/>.= 
<font color="Maroon" title="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">a'</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c6">a</font></span>)</span>
<b>by </b><i><a class="txt" href="altcat_4.html#E2:30"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="altcat_4.html#E3:30"><i><font color="Green" title="E20">A3</font></i></a>, <a class="ref" href="functor0.html#D24" title="FUNCTOR0:def.24">FUNCTOR0:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="functor0.html#K5" title="FUNCTOR0:func.5">Morph-Map</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c4">o1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">a'</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c6">a</font></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#D16" title="FUNCTOR0:def.16">FUNCTOR0:def 16</a></i>
;<br/>
<b>hence </b><a NAME="E18:30"/>
<font color="Maroon" title="c9">a'</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c4">o1</font>
 <b>by </b><i><a class="txt" href="altcat_4.html#E14:30"><i><font color="Green" title="E27">A10</font></i></a>, <a class="txt" href="altcat_4.html#E16:30"><i><font color="Green" title="E28">A11</font></i></a>, <a class="ref" href="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_3.html#D1" title="ALTCAT_3:def.1">ALTCAT_3:def 1</a> <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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