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<span class="kw">let </span><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">H</font> be   <a href="vectsp_1.html#NM1" title="VECTSP_1:NM.1">AddGroup</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being   <a href="grcat_1.html#V2" title="GRCAT_1:attr.2">strict</a>   <a href="grcat_1.html#L1" title="GRCAT_1:struct.1">GroupMorphismStr</a>   st  <a href="grcat_1.html#K8" title="GRCAT_1:func.8">dom</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font> &amp;  <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> &amp;  <a href="grcat_1.html#K10" title="GRCAT_1:func.10">fun</a> <font color="Olive" title="b1">f</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  holds <br/><font color="Olive" title="b1">f</font> is   <a href="grcat_1.html#V2" title="GRCAT_1:attr.2">strict</a>   <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be   <a href="grcat_1.html#V2" title="GRCAT_1:attr.2">strict</a>   <a href="grcat_1.html#L1" title="GRCAT_1:struct.1">GroupMorphismStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="grcat_1.html#K8" title="GRCAT_1:func.8">dom</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font> &amp;  <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> &amp;  <a href="grcat_1.html#K10" title="GRCAT_1:func.10">fun</a> <font color="Maroon" title="c3">f</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  implies <font color="Maroon" title="c3">f</font> is   <a href="grcat_1.html#V2" title="GRCAT_1:attr.2">strict</a>   <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:29"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
(  <a href="grcat_1.html#K8" title="GRCAT_1:func.8">dom</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font> &amp;  <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> )
 <span class="kw">and </span><br/><a NAME="E2:29"/><span class="lab"><font color="Green" title="E12">A2</font></span>: 
 <a href="grcat_1.html#K10" title="GRCAT_1:func.10">fun</a> <font color="Maroon" title="c3">f</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">f</font> is   <a href="grcat_1.html#V2" title="GRCAT_1:attr.2">strict</a>   <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c4">f9</font> = <font color="Maroon" title="c3">f</font> as   <a href="grcat_1.html#V2" title="GRCAT_1:attr.2">strict</a>  <a href="grcat_1.html#NM1" title="GRCAT_1:NM.1">GroupMorphism</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:29"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="grcat_1.html#D13" target="_self" title="GRCAT_1:def.13">Def18</a></span>;<br/>
<a NAME="E4:29"/>
<font color="Maroon" title="c4">f9</font> is   <a href="grcat_1.html#V2" title="GRCAT_1:attr.2">strict</a>   <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="grcat_1.html#D14" target="_self" title="GRCAT_1:def.14">Def19</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:29"/>
<font color="Maroon" title="c3">f</font> is   <a href="grcat_1.html#V2" title="GRCAT_1:attr.2">strict</a>   <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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