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<span class="kw">let </span><font color="Maroon" title="c1">F</font> be   <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">H</font> being  <a href="vectsp_1.html#NM1" title="VECTSP_1:NM.1">AddGroup</a> ex <font color="Olive" title="b3">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">G</font>,<font color="Olive" title="b2">H</font> st <br/>( <font color="Maroon" title="c1">F</font> is    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Olive" title="b1">G</font>,<font color="Olive" title="b2">H</font> &amp; <font color="Maroon" title="c1">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">G</font>,<font color="Olive" title="b2">H</font>,<font color="Olive" title="b3">f</font> #) &amp; <font color="Olive" title="b3">f</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">H</font> being   <a href="vectsp_1.html#NM1" title="VECTSP_1:NM.1">AddGroup</a><span class="kw"> such that </span><br/><a NAME="E2:48"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c1">F</font> is    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="grcat_1.html#T24" target="_self" title="GRCAT_1:th.24">Th24</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">F9</font> = <font color="Maroon" title="c1">F</font> as    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:48"><span class="lab"><font color="Green" title="E15">A1</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font><span class="kw"> such that </span><br/><a NAME="E5:48"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
( <font color="Maroon" title="c4">F9</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">G</font>,<font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c5">f</font> #) &amp; <font color="Maroon" title="c5">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/>
<span class="kw">take </span>
<font color="Maroon" title="c2">G</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">H</font> being  <a href="vectsp_1.html#NM1" title="VECTSP_1:NM.1">AddGroup</a> 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="c2">G</font>,<font color="Olive" title="b1">H</font> st <br/>( <font color="Maroon" title="c1">F</font> is    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Olive" title="b1">H</font> &amp; <font color="Maroon" title="c1">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="c2">G</font>,<font color="Olive" title="b1">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/>

<span class="kw">take </span>
<font color="Maroon" title="c3">H</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c2">G</font>,<font color="Maroon" title="c3">H</font> st <br/>( <font color="Maroon" title="c1">F</font> is    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font> &amp; <font color="Maroon" title="c1">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="c2">G</font>,<font color="Maroon" title="c3">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/>

<span class="kw">take </span>
<font color="Maroon" title="c5">f</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="c1">F</font> is    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font> &amp; <font color="Maroon" title="c1">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="c2">G</font>,<font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c5">f</font> #) &amp; <font color="Maroon" title="c5">f</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E6:48"/>
( <font color="Maroon" title="c1">F</font> is    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font> &amp; <font color="Maroon" title="c1">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="c2">G</font>,<font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c5">f</font> #) &amp; <font color="Maroon" title="c5">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="txt" href="#E5:48"><span class="lab"><font color="Green" title="E16">A2</font></span></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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