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<b>let </b><font color="Maroon">K</font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">L</font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">J</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">K</font>,<font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">V</font> be   <a href="vectsp_2.html#NM6">LeftMod</a> of <font color="Maroon">K</font>;<br/><b>let </b><font color="Maroon">W</font> be   <a href="vectsp_2.html#NM6">LeftMod</a> of <font color="Maroon">L</font>;<br/>









<b>set </b><font color="Maroon">z</font> =  <a href="mod_4.html#K8" target="_self">ZeroMap</a> <font color="Maroon">V</font>,<font color="Maroon">W</font>;<br/>
<a NAME="E1:89"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font> holds  <span class="p1">(<span class="default"><a href="mod_4.html#K8" target="_self">ZeroMap</a> <font color="Maroon">V</font>,<font color="Maroon">W</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="rlvect_1.html#K4">+</a> <font color="Olive">y</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mod_4.html#K8" target="_self">ZeroMap</a> <font color="Maroon">V</font>,<font color="Maroon">W</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mod_4.html#K8" target="_self">ZeroMap</a> <font color="Maroon">V</font>,<font color="Maroon">W</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="mod_4.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E2:89"/>
for <font color="Olive">a</font> being  <a href="vectsp_1.html#NM3">Scalar</a> of <font color="Maroon">K</font><br/> for <font color="Olive">x</font> being  <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font> holds  <span class="p1">(<span class="default"><a href="mod_4.html#K8" target="_self">ZeroMap</a> <font color="Maroon">V</font>,<font color="Maroon">W</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">a</font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">J</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font></span>)</span> <a href="vectsp_1.html#K6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mod_4.html#K8" target="_self">ZeroMap</a> <font color="Maroon">V</font>,<font color="Maroon">W</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="mod_4.html#T12" target="_self">Th12</a></i>;<br/>
<b>hence </b><a NAME="E3:89"/>
 <a href="mod_4.html#K8" target="_self">ZeroMap</a> <font color="Maroon">V</font>,<font color="Maroon">W</font> is    <a href="mod_4.html#M2" target="_self">Homomorphism</a> of <font color="Maroon">J</font>,<font color="Maroon">V</font>,<font color="Maroon">W</font>
 <b>by </b><i><a class="ref" href="mod_4.html#T13" target="_self">Th13</a>, </i>;<br/>


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