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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="vectsp_2.html#NM6">LeftMod</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="mod_2.html#M1" target="_self">Morphism</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="mod_2.html#M1" target="_self">Morphism</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>















<b>assume </b><a NAME="E1:32"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="mod_2.html#G1" target="_self">LModMorphismStr</a>(# <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> #) &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="mod_2.html#G1" target="_self">LModMorphismStr</a>(# <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> #) )
 ;<br/>

 <a href="mod_2.html#K2" target="_self">dom</a> <font color="Maroon">c<sub>5</sub></font> = 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="mod_2.html#D11" target="_self">Def11</a></i>
<br/>.= 
 <a href="mod_2.html#K3" target="_self">cod</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="ref" href="mod_2.html#D11" target="_self">Def11</a></i>
;<br/>
<a NAME="E3:32"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="mod_2.html#K8" target="_self">*</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="mod_2.html#G1" target="_self">LModMorphismStr</a>(# <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> #)
 
<b>by </b><i><a class="txt" href="mod_2.html#E1:32"><i><font color="Green">E20</font></i></a>, <a class="ref" href="mod_2.html#D13" target="_self">Def13</a></i>;<br/>
<b>hence </b><a NAME="E4:32"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="mod_2.html#K9" target="_self">*'</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="mod_2.html#G1" target="_self">LModMorphismStr</a>(# <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> #) &amp; <font color="Maroon">c<sub>5</sub></font> <a href="mod_2.html#K8" target="_self">*</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="mod_2.html#G1" target="_self">LModMorphismStr</a>(# <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> #) )
 ;<br/>


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