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

<b>let </b><font color="Maroon" title="c1">R</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/><b>let </b><font color="Maroon" title="c2">G2</font>, <font color="Maroon" title="c3">G3</font>, <font color="Maroon" title="c4">G1</font> be   <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">R</font>;<br/><b>let </b><font color="Maroon" title="c5">G</font> be    <a href="mod_2.html#M1" title="MOD_2:mode.1">Morphism</a> of <font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c3">G3</font>;<br/><b>let </b><font color="Maroon" title="c6">F</font> be    <a href="mod_2.html#M1" title="MOD_2:mode.1">Morphism</a> of <font color="Maroon" title="c4">G1</font>,<font color="Maroon" title="c2">G2</font>;<br/><b>let </b><font color="Maroon" title="c7">g</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c3">G3</font>;<br/><b>let </b><font color="Maroon" title="c8">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c4">G1</font>,<font color="Maroon" title="c2">G2</font>;<br/>















<b>assume </b><a NAME="E1:32"/><i><font color="Green" title="E20">A1</font></i>: 
( <font color="Maroon" title="c5">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c3">G3</font>,<font color="Maroon" title="c7">g</font> #) &amp; <font color="Maroon" title="c6">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <font color="Maroon" title="c4">G1</font>,<font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c8">f</font> #) )
 ;<br/>

 <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c5">G</font> = 
<font color="Maroon" title="c2">G2</font>
<b>by </b><i><a class="ref" href="mod_2.html#D11" target="_self" title="MOD_2:def.11">Def11</a></i>
<br/>.= 
 <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c6">F</font>
<b>by </b><i><a class="ref" href="mod_2.html#D11" target="_self" title="MOD_2:def.11">Def11</a></i>
;<br/>
<a NAME="E3:32"/><b>then </b>
<font color="Maroon" title="c5">G</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c6">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <font color="Maroon" title="c4">G1</font>,<font color="Maroon" title="c3">G3</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">f</font></span>)</span> #)
 
<b>by </b><i><a class="txt" href="mod_2.html#E1:32"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="mod_2.html#D13" target="_self" title="MOD_2:def.13">Def13</a></i>;<br/>
<b>hence </b><a NAME="E4:32"/>
( <font color="Maroon" title="c5">G</font> <a href="mod_2.html#K9" title="MOD_2:func.9">*'</a> <font color="Maroon" title="c6">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <font color="Maroon" title="c4">G1</font>,<font color="Maroon" title="c3">G3</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">f</font></span>)</span> #) &amp; <font color="Maroon" title="c5">G</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c6">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#G1" title="MOD_2:aggr.1">LModMorphismStr</a>(# <font color="Maroon" title="c4">G1</font>,<font color="Maroon" title="c3">G3</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">f</font></span>)</span> #) )
 ;<br/>


</div>
