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<b>let </b><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">H</font> be   <a href="algstr_1.html#NM2" title="ALGSTR_1:NM.2">AddGroup</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">F</font> being   <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>  ex <font color="Olive" title="b2">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font> st <br/>(  <a href="grcat_1.html#G1" title="GRCAT_1:aggr.1">GroupMorphismStr</a>(# the <a href="grcat_1.html#U1" title="GRCAT_1:sel.1">Source</a> of <font color="Olive" title="b1">F</font>,the <a href="grcat_1.html#U2" title="GRCAT_1:sel.2">Target</a> of <font color="Olive" title="b1">F</font>,the <a href="grcat_1.html#U3" title="GRCAT_1:sel.3">Fun</a> of <font color="Olive" title="b1">F</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#G1" title="GRCAT_1:aggr.1">GroupMorphismStr</a>(# <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font>,<font color="Olive" title="b2">f</font> #) &amp; <font color="Olive" title="b2">f</font> is <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a> )</span><br/><b>let </b><font color="Maroon" title="c3">F</font> be    <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font> st <br/>(  <a href="grcat_1.html#G1" title="GRCAT_1:aggr.1">GroupMorphismStr</a>(# the <a href="grcat_1.html#U1" title="GRCAT_1:sel.1">Source</a> of <font color="Maroon" title="c3">F</font>,the <a href="grcat_1.html#U2" title="GRCAT_1:sel.2">Target</a> of <font color="Maroon" title="c3">F</font>,the <a href="grcat_1.html#U3" title="GRCAT_1:sel.3">Fun</a> of <font color="Maroon" title="c3">F</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#G1" title="GRCAT_1:aggr.1">GroupMorphismStr</a>(# <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font>,<font color="Olive" title="b1">f</font> #) &amp; <font color="Olive" title="b1">f</font> is <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a> )</span><br/>





<i><font color="Green" title="E18">A1</font></i>: the <a href="grcat_1.html#U1" title="GRCAT_1:sel.1">Source</a> of <font color="Maroon" title="c3">F</font> = 
 <a href="grcat_1.html#K8" title="GRCAT_1:func.8">dom</a> <font color="Maroon" title="c3">F</font>

<br/>.= 
<font color="Maroon" title="c1">G</font>
<b>by </b><i><a class="ref" href="grcat_1.html#D19" target="_self" title="GRCAT_1:def.19">Def19</a></i>
;<br/>
<i><font color="Green" title="E19">A2</font></i>: the <a href="grcat_1.html#U2" title="GRCAT_1:sel.2">Target</a> of <font color="Maroon" title="c3">F</font> = 
 <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Maroon" title="c3">F</font>

<br/>.= 
<font color="Maroon" title="c2">H</font>
<b>by </b><i><a class="ref" href="grcat_1.html#D19" target="_self" title="GRCAT_1:def.19">Def19</a></i>
;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">f</font> = the <a href="grcat_1.html#U3" title="GRCAT_1:sel.3">Fun</a> of <font color="Maroon" title="c3">F</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font> <b>by </b><i><a class="txt" href="grcat_1.html#E1:37"><i><font color="Green" title="E18">A1</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">f</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="grcat_1.html#G1" title="GRCAT_1:aggr.1">GroupMorphismStr</a>(# the <a href="grcat_1.html#U1" title="GRCAT_1:sel.1">Source</a> of <font color="Maroon" title="c3">F</font>,the <a href="grcat_1.html#U2" title="GRCAT_1:sel.2">Target</a> of <font color="Maroon" title="c3">F</font>,the <a href="grcat_1.html#U3" title="GRCAT_1:sel.3">Fun</a> of <font color="Maroon" title="c3">F</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#G1" title="GRCAT_1:aggr.1">GroupMorphismStr</a>(# <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c4">f</font> #) &amp; <font color="Maroon" title="c4">f</font> is <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a> )</span><br/>

<b>thus </b><a NAME="E4:37"/>
(  <a href="grcat_1.html#G1" title="GRCAT_1:aggr.1">GroupMorphismStr</a>(# the <a href="grcat_1.html#U1" title="GRCAT_1:sel.1">Source</a> of <font color="Maroon" title="c3">F</font>,the <a href="grcat_1.html#U2" title="GRCAT_1:sel.2">Target</a> of <font color="Maroon" title="c3">F</font>,the <a href="grcat_1.html#U3" title="GRCAT_1:sel.3">Fun</a> of <font color="Maroon" title="c3">F</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#G1" title="GRCAT_1:aggr.1">GroupMorphismStr</a>(# <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c4">f</font> #) &amp; <font color="Maroon" title="c4">f</font> is <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a> )
 <b>by </b><i><a class="txt" href="grcat_1.html#E1:37"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="grcat_1.html#E2:37"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="grcat_1.html#T18" target="_self" title="GRCAT_1:th.18">Th18</a></i>; <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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