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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font>, <font color="Maroon" title="c3">G3</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">G</font> being   <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c3">G3</font><br/> for <font color="Olive" title="b2">F</font> being   <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font> holds  <font color="Olive" title="b1">G</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Olive" title="b2">F</font> is    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c3">G3</font></span><br/><b>let </b><font color="Maroon" title="c4">G</font> be    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c3">G3</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="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font> holds  <font color="Maroon" title="c4">G</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Olive" title="b1">F</font> is    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c3">G3</font></span><br/><b>let </b><font color="Maroon" title="c5">F</font> be    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">G</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Maroon" title="c5">F</font> is    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c3">G3</font></span><br/>





<b>consider </b><font color="Maroon" title="c6">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c3">G3</font><b> such that </b><br/><a NAME="E2:43"/><i><font color="Green" title="E23">A1</font></i>: 
 <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="c4">G</font>,the <a href="grcat_1.html#U2" title="GRCAT_1:sel.2">Target</a> of <font color="Maroon" title="c4">G</font>,the <a href="grcat_1.html#U3" title="GRCAT_1:sel.3">Fun</a> of <font color="Maroon" title="c4">G</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="c2">G2</font>,<font color="Maroon" title="c3">G3</font>,<font color="Maroon" title="c6">g</font> #)
 <b>and </b><br/><a NAME="E3:43"/>
<font color="Maroon" title="c6">g</font> is <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>
 <b>by </b><i><a class="ref" href="grcat_1.html#T22" target="_self" title="GRCAT_1:th.22">Th22</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font><b> such that </b><br/><a NAME="E5:43"/><i><font color="Green" title="E24">A2</font></i>: 
 <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="c5">F</font>,the <a href="grcat_1.html#U2" title="GRCAT_1:sel.2">Target</a> of <font color="Maroon" title="c5">F</font>,the <a href="grcat_1.html#U3" title="GRCAT_1:sel.3">Fun</a> of <font color="Maroon" title="c5">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">G1</font>,<font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c7">f</font> #)
 <b>and </b><br/><a NAME="E6:43"/>
<font color="Maroon" title="c7">f</font> is <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>
 <b>by </b><i><a class="ref" href="grcat_1.html#T22" target="_self" title="GRCAT_1:th.22">Th22</a></i>;<br/>
 <a href="grcat_1.html#K8" title="GRCAT_1:func.8">dom</a> <font color="Maroon" title="c4">G</font> = 
<font color="Maroon" title="c2">G2</font>
<b>by </b><i><a class="ref" href="grcat_1.html#D19" target="_self" title="GRCAT_1:def.19">Def19</a></i>
<br/>.= 
 <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Maroon" title="c5">F</font>
<b>by </b><i><a class="ref" href="grcat_1.html#D19" target="_self" title="GRCAT_1:def.19">Def19</a></i>
;<br/>
<a NAME="E8:43"/><b>then </b>
<font color="Maroon" title="c4">G</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Maroon" title="c5">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">G1</font>,<font color="Maroon" title="c3">G3</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">f</font></span>)</span> #)
 
<b>by </b><i><a class="txt" href="#E2:43"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="#E5:43"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="grcat_1.html#D21" target="_self" title="GRCAT_1:def.21">Def21</a></i>;<br/>
<a NAME="E9:43"/><b>then </b>
(  <a href="grcat_1.html#K8" title="GRCAT_1:func.8">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G1</font> &amp;  <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">G3</font> )
 
;<br/>
<b>hence </b><a NAME="E10:43"/>
<font color="Maroon" title="c4">G</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Maroon" title="c5">F</font> is    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c3">G3</font>
 <b>by </b><i><a class="ref" href="grcat_1.html#D19" target="_self" title="GRCAT_1:def.19">Def19</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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