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<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">f</font>, <font color="Maroon" title="c3">g</font> be  <a href="mod_2.html#V2" title="MOD_2:attr.2">strict</a> <a href="mod_2.html#NM1" title="MOD_2:NM.1">LModMorphism</a> of <font color="Maroon" title="c1">R</font>;<br/>



<b>assume </b><a NAME="E1:34"/>
 <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c2">f</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">G1</font>, <font color="Maroon" title="c5">G2</font>, <font color="Maroon" title="c6">G3</font> being   <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">R</font>, <font color="Maroon" title="c7">f0</font> being   <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="c5">G2</font>, <font color="Maroon" title="c8">g0</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c5">G2</font>,<font color="Maroon" title="c6">G3</font><b> such that </b><br/><a NAME="E3:34"/><i><font color="Green" title="E21">A1</font></i>: 
( <font color="Maroon" title="c2">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="c5">G2</font>,<font color="Maroon" title="c7">f0</font> #) &amp; <font color="Maroon" title="c3">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="c5">G2</font>,<font color="Maroon" title="c6">G3</font>,<font color="Maroon" title="c8">g0</font> #) &amp; <font color="Maroon" title="c3">g</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c2">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="c6">G3</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">g0</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">f0</font></span>)</span> #) )
 <b>by </b><i><a class="ref" href="mod_2.html#T22" target="_self" title="MOD_2:th.22">Th22</a></i>;<br/>
<b>thus </b><a NAME="E4:34"/>
 <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c2">f</font>
 <b>by </b><i><a class="txt" href="mod_2.html#E3:34"><i><font color="Green" title="E21">A1</font></i></a></i>;<br/>

<b>thus </b><a NAME="E5:34"/>
 <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c3">g</font>
 <b>by </b><i><a class="txt" href="mod_2.html#E3:34"><i><font color="Green" title="E21">A1</font></i></a></i>;<br/>


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