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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">H</font> being  <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">R</font><br/> for <font color="Olive" title="b3">f</font> being   <a href="mod_2.html#L1" title="MOD_2:struct.1">LModMorphismStr</a> of <font color="Maroon" title="c1">R</font>  st  <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">G</font> &amp;  <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H</font> &amp;  <a href="mod_2.html#K4" title="MOD_2:func.4">fun</a> <font color="Olive" title="b3">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> holds <br/><font color="Olive" title="b3">f</font> is    <a href="mod_2.html#M1" title="MOD_2:mode.1">Morphism</a> of <font color="Olive" title="b1">G</font>,<font color="Olive" title="b2">H</font></span><br/><b>let </b><font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">H</font> be   <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being   <a href="mod_2.html#L1" title="MOD_2:struct.1">LModMorphismStr</a> of <font color="Maroon" title="c1">R</font>  st  <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font> &amp;  <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H</font> &amp;  <a href="mod_2.html#K4" title="MOD_2:func.4">fun</a> <font color="Olive" title="b1">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> holds <br/><font color="Olive" title="b1">f</font> is    <a href="mod_2.html#M1" title="MOD_2:mode.1">Morphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font></span><br/><b>let </b><font color="Maroon" title="c4">f</font> be    <a href="mod_2.html#L1" title="MOD_2:struct.1">LModMorphismStr</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font> &amp;  <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H</font> &amp;  <a href="mod_2.html#K4" title="MOD_2:func.4">fun</a> <font color="Maroon" title="c4">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> implies <font color="Maroon" title="c4">f</font> is    <a href="mod_2.html#M1" title="MOD_2:mode.1">Morphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font> )</span><br/>







<b>assume </b><a NAME="E1:18"/><i><font color="Green" title="E10">A1</font></i>: 
(  <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font> &amp;  <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H</font> &amp;  <a href="mod_2.html#K4" title="MOD_2:func.4">fun</a> <font color="Maroon" title="c4">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">f</font> is    <a href="mod_2.html#M1" title="MOD_2:mode.1">Morphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c5">f'</font> = <font color="Maroon" title="c4">f</font> as   <a href="mod_2.html#NM1" title="MOD_2:NM.1">LModMorphism</a> of <font color="Maroon" title="c1">R</font> <b>by </b><i><a class="ref" href="mod_2.html#D10" target="_self" title="MOD_2:def.10">Def10</a></i>;<br/>
<a NAME="E3:18"/>
<font color="Maroon" title="c5">f'</font> is    <a href="mod_2.html#M1" title="MOD_2:mode.1">Morphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font>
 
<b>by </b><i><a class="txt" href="#E1:18"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="mod_2.html#D11" target="_self" title="MOD_2:def.11">Def11</a></i>;<br/>
<b>hence </b><a NAME="E4:18"/>
<font color="Maroon" title="c4">f</font> is    <a href="mod_2.html#M1" title="MOD_2:mode.1">Morphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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