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<span class="kw">let </span><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font>, <font color="Maroon" title="c3">G3</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="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>





<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E2:52"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
 <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> #)
 <span class="kw">and </span><br/><a NAME="E3:52"/>
<font color="Maroon" title="c6">g</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="grcat_1.html#T22" target="_self" title="GRCAT_1:th.22">Th22</a></span>;<br/>
<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E5:52"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
 <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> #)
 <span class="kw">and </span><br/><a NAME="E6:52"/>
<font color="Maroon" title="c7">f</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="grcat_1.html#T22" target="_self" title="GRCAT_1:th.22">Th22</a></span>;<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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="grcat_1.html#D19" target="_self" title="GRCAT_1:def.19">Def19</a></span>
<br/>.= 
 <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Maroon" title="c5">F</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="grcat_1.html#D19" target="_self" title="GRCAT_1:def.19">Def19</a></span>
;<br/>
<a NAME="E8:52"/><span class="kw">then </span>
<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> #)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:52"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E5:52"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="grcat_1.html#D21" target="_self" title="GRCAT_1:def.21">Def21</a></span>;<br/>
<a NAME="E9:52"/><span class="kw">then </span>
(  <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/>
<span class="kw">hence </span><a NAME="E10:52"/>
<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 class="kw">by</span> <span class="lab"><a class="ref" href="grcat_1.html#D19" target="_self" title="GRCAT_1:def.19">Def19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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