<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">C1</font>, <font color="Maroon" title="c2">C2</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">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#V10" title="FUNCTOR0:attr.10">Covariant</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/>





<a NAME="E1:50"/>
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#V1" title="FUNCTOR0:attr.1">Covariant</a>
 
<b>by </b><i><a class="ref" href="functor0.html#D13" target="_self" title="FUNCTOR0:def.13">Def13</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c6">f</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">C1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font><b> such that </b><br/><a NAME="E3:50"/><i><font color="Green" title="E37">A1</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> <span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c6">f</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#D2" target="_self" title="FUNCTOR0:def.2">Def2</a></i>;<br/>
<i><font color="Green" title="E38">A2</font></i>: <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 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="c6">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">o1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">o1</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> 
<b>by </b><i><a class="txt" href="functor0.html#E3:50"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="funct_3.html#T96" title="FUNCT_3:th.96">FUNCT_3:96</a></i>
<br/>.= 
<font color="Maroon" title="c6">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">o1</font>
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
;<br/>
<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 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="c6">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">o2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">o2</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> 
<b>by </b><i><a class="txt" href="functor0.html#E3:50"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="funct_3.html#T96" title="FUNCT_3:th.96">FUNCT_3:96</a></i>
<br/>.= 
<font color="Maroon" title="c6">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">o2</font>
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
;<br/>
<b>hence </b><a NAME="E6:50"/>
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="c4">o1</font>,<font color="Maroon" title="c5">o2</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="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c4">o1</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="c5">o2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="txt" href="functor0.html#E3:50"><i><font color="Green" title="E37">A1</font></i></a>, <a class="txt" href="functor0.html#E4:50"><i><font color="Green" title="E38">A2</font></i></a>, <a class="ref" href="funct_3.html#T96" title="FUNCT_3:th.96">FUNCT_3:96</a></i>;<br/>


</div>
