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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#V3" title="STRUCT_0:attr.3">empty</a>  <a href="altcat_1.html#L1" title="ALTCAT_1:struct.1">AltGraph</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">A</font>,<font color="Maroon" title="c2">B</font>;<br/>



<b>given </b><font color="Maroon" title="c4">f</font> being    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c1">A</font>,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#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font><b> such that </b><a NAME="E1:48"/><i><font color="Green" title="E32">A1</font></i>: 
( <font color="Maroon" title="c4">f</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c3">F</font> &amp; <font color="Maroon" title="c4">f</font> is <a href="msualg_3.html#V2" title="MSUALG_3:attr.2">"onto"</a> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="functor0.html#D33" title="FUNCTOR0:def.33">FUNCTOR0:def 33</a>,<a class="ref" href="functor0.html#D35" title="FUNCTOR0:def.35">FUNCTOR0:def 35</a><br/>

<b>assume </b><a NAME="E2:48"/><i><font color="Green" title="E33">A2</font></i>: 
 <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">rng</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="functor0.html#D8" title="FUNCTOR0:def.8">FUNCTOR0:def 8</a>,<a class="ref" href="funct_2.html#D3" title="FUNCT_2:def.3">FUNCT_2:def 3</a><br/>

<a NAME="E3:48"/><i><font color="Green" title="E34">A3</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</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>let </b><font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">b</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">B</font>;<br/>

<b>assume </b><a NAME="E4:48"/><i><font color="Green" title="E35">A4</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">a</font>,<font color="Maroon" title="c6">b</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>let </b><font color="Maroon" title="c7">f</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font>;<br/>

<a NAME="E5:48"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">rng</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font>
 
<b>by </b><i><a class="txt" href="yellow20.html#E2:48"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c8">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E7:48"/><i><font color="Green" title="E36">A5</font></i>: 
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> )
 <b>by </b><i><a class="txt" href="yellow20.html#E3:48"><i><font color="Green" title="E34">A3</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">d</font>, <font color="Maroon" title="c10">c</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E9:48"/><i><font color="Green" title="E37">A6</font></i>: 
( <font color="Maroon" title="c9">d</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="c1">A</font> &amp; <font color="Maroon" title="c10">c</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="c1">A</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">d</font>,<font color="Maroon" title="c10">c</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">x</font> )
 <b>by </b><i><a class="txt" href="yellow20.html#E7:48"><i><font color="Green" title="E36">A5</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">c</font> = <font color="Maroon" title="c10">c</font>, <font color="Maroon" title="c12">d</font> = <font color="Maroon" title="c9">d</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font> <b>by </b><i><a class="txt" href="yellow20.html#E9:48"><i><font color="Green" title="E37">A6</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c12">d</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c11">c</font>
;<br/>

<a NAME="E11:48"/>
the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> is <a href="functor0.html#V2" title="FUNCTOR0:attr.2">Contravariant</a>
 
<b>by </b><i><a class="ref" href="functor0.html#D14" title="FUNCTOR0:def.14">FUNCTOR0:def 14</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c13">g</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font><b> such that </b><br/><a NAME="E13:48"/><i><font color="Green" title="E38">A7</font></i>: 
the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="functor0.html#K1" title="FUNCTOR0:func.1">~</a> <span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Maroon" title="c13">g</font>,<font color="Maroon" title="c13">g</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span>
 <b>by </b><i><a class="ref" href="functor0.html#D3" title="FUNCTOR0:def.3">FUNCTOR0:def 3</a></i>;<br/>
<a NAME="E14:48"/><i><font color="Green" title="E39">A8</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c11">c</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c11">c</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c12">d</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<a NAME="E15:48"/>
( the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c11">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Maroon" title="c13">g</font>,<font color="Maroon" title="c13">g</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c11">c</font> &amp; the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Maroon" title="c13">g</font>,<font color="Maroon" title="c13">g</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c12">d</font> )
 
<b>by </b><i><a class="txt" href="yellow20.html#E13:48"><i><font color="Green" title="E38">A7</font></i></a>, <a class="txt" href="yellow20.html#E14:48"><i><font color="Green" title="E39">A8</font></i></a>, <a class="ref" href="funct_4.html#T44" title="FUNCT_4:th.44">FUNCT_4:44</a></i>;<br/>
<a NAME="E16:48"/><b>then </b>
( the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c11">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">c</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">c</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">d</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">d</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 
<b>by </b><i><a class="ref" href="funct_3.html#T96" title="FUNCT_3:th.96">FUNCT_3:96</a></i>;<br/>
<a NAME="E17:48"/><b>then </b>
( <font color="Maroon" title="c3">F</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"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">c</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">c</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  &amp; <font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">d</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">d</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  )
 
;<br/>
<a NAME="E18:48"/><b>then </b><i><font color="Green" title="E40">A9</font></i>: 
( <font color="Maroon" title="c3">F</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> <font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">c</font> &amp; <font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">d</font> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>
<i><font color="Green" title="E41">A10</font></i>: the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c11">c</font> = 
<span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Maroon" title="c13">g</font>,<font color="Maroon" title="c13">g</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c11">c</font>,<font color="Maroon" title="c12">d</font>
<b>by </b><i><a class="txt" href="yellow20.html#E13:48"><i><font color="Green" title="E38">A7</font></i></a>, <a class="txt" href="yellow20.html#E14:48"><i><font color="Green" title="E39">A8</font></i></a>, <a class="ref" href="funct_4.html#T44" title="FUNCT_4:th.44">FUNCT_4:44</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</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="c11">c</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="c12">d</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="yellow20.html#E18:48"><i><font color="Green" title="E40">A9</font></i></a>, <a class="ref" href="funct_3.html#T96" title="FUNCT_3:th.96">FUNCT_3:96</a></i>
;<br/>
<a NAME="E20:48"/><b>then </b><i><font color="Green" title="E42">A11</font></i>: 
( <font color="Maroon" title="c5">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="Maroon" title="c11">c</font> &amp; <font color="Maroon" title="c6">b</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="Maroon" title="c12">d</font> )
 
<b>by </b><i><a class="txt" href="yellow20.html#E7:48"><i><font color="Green" title="E36">A5</font></i></a>, <a class="txt" href="yellow20.html#E9:48"><i><font color="Green" title="E37">A6</font></i></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/>
 <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="c12">d</font>,<font color="Maroon" title="c11">c</font></span>)</span> = 
<span class="p1">(<span class="default">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#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c11">c</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="yellow20.html#E1:48"><i><font color="Green" title="E32">A1</font></i></a>, <a class="txt" href="yellow20.html#E7:48"><i><font color="Green" title="E36">A5</font></i></a>, <a class="txt" href="yellow20.html#E9:48"><i><font color="Green" title="E37">A6</font></i></a>, <a class="ref" href="msualg_3.html#D3" title="MSUALG_3:def.3">MSUALG_3:def 3</a></i>
<br/>.= 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
<b>by </b><i><a class="txt" href="yellow20.html#E7:48"><i><font color="Green" title="E36">A5</font></i></a>, <a class="txt" href="yellow20.html#E9:48"><i><font color="Green" title="E37">A6</font></i></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
;<br/>
<b>then consider </b><font color="Maroon" title="c14">g</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E23:48"/><i><font color="Green" title="E43">A12</font></i>: 
( <font color="Maroon" title="c14">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">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="c12">d</font>,<font color="Maroon" title="c11">c</font></span>)</span> &amp; <font color="Maroon" title="c7">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="Maroon" title="c12">d</font>,<font color="Maroon" title="c11">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">g</font> )
 <b>by </b><i><a class="txt" href="yellow20.html#E4:48"><i><font color="Green" title="E35">A4</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="c15">g</font> = <font color="Maroon" title="c14">g</font> as   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c11">c</font> <b>by </b><i><a class="txt" href="yellow20.html#E23:48"><i><font color="Green" title="E43">A12</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c15">g</font>
;<br/>

<b>thus </b><a NAME="E25:48"/>
( <font color="Maroon" title="c6">b</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="Maroon" title="c12">d</font> &amp; <font color="Maroon" title="c5">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="Maroon" title="c11">c</font> &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c12">d</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>  )
 <b>by </b><i><a class="txt" href="yellow20.html#E7:48"><i><font color="Green" title="E36">A5</font></i></a>, <a class="txt" href="yellow20.html#E9:48"><i><font color="Green" title="E37">A6</font></i></a>, <a class="txt" href="yellow20.html#E19:48"><i><font color="Green" title="E41">A10</font></i></a>, <a class="txt" href="yellow20.html#E23:48"><i><font color="Green" title="E43">A12</font></i></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/>

<b>thus </b><a NAME="E26:48"/>
<font color="Maroon" title="c7">f</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="c15">g</font>
 <b>by </b><i><a class="txt" href="yellow20.html#E4:48"><i><font color="Green" title="E35">A4</font></i></a>, <a class="txt" href="yellow20.html#E20:48"><i><font color="Green" title="E42">A11</font></i></a>, <a class="txt" href="yellow20.html#E23:48"><i><font color="Green" title="E43">A12</font></i></a>, <a class="ref" href="functor0.html#D17" title="FUNCTOR0:def.17">FUNCTOR0:def 17</a></i>;<br/>


</div>
