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<b>consider </b><font color="Maroon" title="c3">G1'</font>, <font color="Maroon" title="c4">G2'</font>, <font color="Maroon" title="c5">G3'</font> being   <a href="algstr_1.html#NM2" title="ALGSTR_1:NM.2">AddGroup</a><b> such that </b><br/><a NAME="E2:42_1_1"/><i><font color="Green" title="E22">A2</font></i>: 
<font color="Maroon" title="c1">G</font> is    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c4">G2'</font>,<font color="Maroon" title="c5">G3'</font>
 <b>and </b><br/><a NAME="E3:42_1_1"/><i><font color="Green" title="E23">A3</font></i>: 
<font color="Maroon" title="c2">F</font> is    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">G1'</font>,<font color="Maroon" title="c4">G2'</font>
 <b>by </b><i><a class="txt" href="#E1:42"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="grcat_1.html#T26" target="_self" title="GRCAT_1:th.26">Th26</a></i>;<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="c4">G2'</font>,<font color="Maroon" title="c5">G3'</font><b> such that </b><br/><a NAME="E5:42_1_1"/><i><font color="Green" title="E24">A4</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="c1">G</font>,the <a href="grcat_1.html#U2" title="GRCAT_1:sel.2">Target</a> of <font color="Maroon" title="c1">G</font>,the <a href="grcat_1.html#U3" title="GRCAT_1:sel.3">Fun</a> of <font color="Maroon" title="c1">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="c4">G2'</font>,<font color="Maroon" title="c5">G3'</font>,<font color="Maroon" title="c6">g'</font> #)
 <b>and </b><br/><a NAME="E6:42_1_1"/><i><font color="Green" title="E25">A5</font></i>: 
<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="txt" href="#E2:42_1_1"><i><font color="Green" title="E22">A2</font></i></a>, <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="c3">G1'</font>,<font color="Maroon" title="c4">G2'</font><b> such that </b><br/><a NAME="E8:42_1_1"/><i><font color="Green" title="E26">A6</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="c2">F</font>,the <a href="grcat_1.html#U2" title="GRCAT_1:sel.2">Target</a> of <font color="Maroon" title="c2">F</font>,the <a href="grcat_1.html#U3" title="GRCAT_1:sel.3">Fun</a> of <font color="Maroon" title="c2">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="c3">G1'</font>,<font color="Maroon" title="c4">G2'</font>,<font color="Maroon" title="c7">f'</font> #)
 <b>and </b><br/><a NAME="E9:42_1_1"/><i><font color="Green" title="E27">A7</font></i>: 
<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="txt" href="#E3:42_1_1"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="grcat_1.html#T22" target="_self" title="GRCAT_1:th.22">Th22</a></i>;<br/>
<a NAME="E10:42_1_1"/>
<font color="Maroon" title="c6">g'</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <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="txt" href="#E6:42_1_1"><i><font color="Green" title="E25">A5</font></i></a>, <a class="txt" href="#E9:42_1_1"><i><font color="Green" title="E27">A7</font></i></a>, <a class="ref" href="grcat_1.html#T14" target="_self" title="GRCAT_1:th.14">Th14</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c8">T'</font> =  <a href="grcat_1.html#G1" title="GRCAT_1:aggr.1">GroupMorphismStr</a>(# <font color="Maroon" title="c3">G1'</font>,<font color="Maroon" title="c5">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> #) 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> <b>by </b><i><a class="ref" href="grcat_1.html#T20" target="_self" title="GRCAT_1:th.20">Th20</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c8">T'</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">G1</font>, <font color="Olive" title="b2">G2</font>, <font color="Olive" title="b3">G3</font> being  <a href="algstr_1.html#NM2" title="ALGSTR_1:NM.2">AddGroup</a><br/> for <font color="Olive" title="b4">g</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b2">G2</font>,<font color="Olive" title="b3">G3</font><br/> for <font color="Olive" title="b5">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">G1</font>,<font color="Olive" title="b2">G2</font>  st  <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="c1">G</font>,the <a href="grcat_1.html#U2" title="GRCAT_1:sel.2">Target</a> of <font color="Maroon" title="c1">G</font>,the <a href="grcat_1.html#U3" title="GRCAT_1:sel.3">Fun</a> of <font color="Maroon" title="c1">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="Olive" title="b2">G2</font>,<font color="Olive" title="b3">G3</font>,<font color="Olive" title="b4">g</font> #) &amp;  <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="c2">F</font>,the <a href="grcat_1.html#U2" title="GRCAT_1:sel.2">Target</a> of <font color="Maroon" title="c2">F</font>,the <a href="grcat_1.html#U3" title="GRCAT_1:sel.3">Fun</a> of <font color="Maroon" title="c2">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="Olive" title="b1">G1</font>,<font color="Olive" title="b2">G2</font>,<font color="Olive" title="b5">f</font> #) holds <br/><font color="Maroon" title="c8">T'</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="Olive" title="b1">G1</font>,<font color="Olive" title="b3">G3</font>,<span class="p1">(<span class="default"><font color="Olive" title="b4">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b5">f</font></span>)</span> #)</span><br/>

<b>thus </b><a NAME="E12:42_1_1"/>
for <font color="Olive" title="b1">G1</font>, <font color="Olive" title="b2">G2</font>, <font color="Olive" title="b3">G3</font> being  <a href="algstr_1.html#NM2" title="ALGSTR_1:NM.2">AddGroup</a><br/> for <font color="Olive" title="b4">g</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b2">G2</font>,<font color="Olive" title="b3">G3</font><br/> for <font color="Olive" title="b5">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">G1</font>,<font color="Olive" title="b2">G2</font>  st  <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="c1">G</font>,the <a href="grcat_1.html#U2" title="GRCAT_1:sel.2">Target</a> of <font color="Maroon" title="c1">G</font>,the <a href="grcat_1.html#U3" title="GRCAT_1:sel.3">Fun</a> of <font color="Maroon" title="c1">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="Olive" title="b2">G2</font>,<font color="Olive" title="b3">G3</font>,<font color="Olive" title="b4">g</font> #) &amp;  <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="c2">F</font>,the <a href="grcat_1.html#U2" title="GRCAT_1:sel.2">Target</a> of <font color="Maroon" title="c2">F</font>,the <a href="grcat_1.html#U3" title="GRCAT_1:sel.3">Fun</a> of <font color="Maroon" title="c2">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="Olive" title="b1">G1</font>,<font color="Olive" title="b2">G2</font>,<font color="Olive" title="b5">f</font> #) holds <br/><font color="Maroon" title="c8">T'</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="Olive" title="b1">G1</font>,<font color="Olive" title="b3">G3</font>,<span class="p1">(<span class="default"><font color="Olive" title="b4">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b5">f</font></span>)</span> #)
 <b>by </b><i><a class="txt" href="#E5:42_1_1"><i><font color="Green" title="E24">A4</font></i></a>, <a class="txt" href="#E8:42_1_1"><i><font color="Green" title="E26">A6</font></i></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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