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<b>let </b><font color="Maroon" title="c1">C1</font>, <font color="Maroon" title="c2">C2</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="altcat_1.html#L2" title="ALTCAT_1:struct.2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon" title="c3">F</font> be  <a href="functor0.html#V11" title="FUNCTOR0:attr.11">Contravariant</a>  <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>;<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">C1</font>;<br/><b>let </b><font color="Maroon" title="c6">Fm</font> be   <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>;<br/>







<b>assume </b><a NAME="E1:20"/><i><font color="Green" title="E10">A1</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> 
 ;<br/>

<b>assume </b><a NAME="E2:20"/>
<font color="Maroon" title="c3">F</font> is <a href="functor0.html#V18" title="FUNCTOR0:attr.18">full</a>
 ;<br/>

<a NAME="E3:20"/><b>then </b>
 <a href="functor0.html#K7" title="FUNCTOR0:func.7">Morph-Map</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c5">o2</font> is <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>
 
<b>by </b><i><a class="ref" href="altcat_4.html#T14" target="_self" title="ALTCAT_4:th.14">Th14</a></i>;<br/>
<a NAME="E4:20"/><b>then </b><i><font color="Green" title="E11">A2</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#K7" title="FUNCTOR0:func.7">Morph-Map</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c5">o2</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/>
<b>assume </b><a NAME="E5:20"/>
<font color="Maroon" title="c3">F</font> is <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>
 ;<br/>

<a NAME="E6:20"/><b>then </b><i><font color="Green" title="E12">A3</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#E1:20"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="functor0.html#D20" title="FUNCTOR0:def.20">FUNCTOR0:def 20</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c7">m</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E8:20"/><i><font color="Green" title="E13">A4</font></i>: 
<font color="Maroon" title="c7">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</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="Maroon" title="c4">o1</font>,<font color="Maroon" title="c5">o2</font></span>)</span>
 <b>and </b><br/><a NAME="E9:20"/><i><font color="Green" title="E14">A5</font></i>: 
<font color="Maroon" title="c6">Fm</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="Maroon" title="c4">o1</font>,<font color="Maroon" title="c5">o2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">m</font>
 <b>by </b><i><a class="txt" href="altcat_4.html#E4:20"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">m</font> = <font color="Maroon" title="c7">m</font> as   <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> <b>by </b><i><a class="txt" href="altcat_4.html#E6:20"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="altcat_4.html#E8:20"><i><font color="Green" title="E13">A4</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="c8">m</font>
;<br/>

<b>thus </b><a NAME="E11:20"/>
<font color="Maroon" title="c6">Fm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Maroon" title="c8">m</font>
 <b>by </b><i><a class="txt" href="altcat_4.html#E1:20"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="altcat_4.html#E6:20"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="altcat_4.html#E9:20"><i><font color="Green" title="E14">A5</font></i></a>, <a class="ref" href="functor0.html#D17" title="FUNCTOR0:def.17">FUNCTOR0:def 17</a></i>;<br/>


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