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<b>let </b><font color="Maroon" title="c1">f</font>, <font color="Maroon" title="c2">g</font>, <font color="Maroon" title="c3">h</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="grcat_1.html#K8" title="GRCAT_1:func.8">dom</a> <font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Maroon" title="c2">g</font> &amp;  <a href="grcat_1.html#K8" title="GRCAT_1:func.8">dom</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Maroon" title="c1">f</font> implies <font color="Maroon" title="c3">h</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Maroon" title="c1">f</font> )</span><br/>

<b>assume </b><a NAME="E1:49"/><i><font color="Green" title="E28">A1</font></i>: 
(  <a href="grcat_1.html#K8" title="GRCAT_1:func.8">dom</a> <font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Maroon" title="c2">g</font> &amp;  <a href="grcat_1.html#K8" title="GRCAT_1:func.8">dom</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Maroon" title="c1">f</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">h</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Maroon" title="c1">f</font></span><br/>

<b>set </b><font color="Maroon" title="c4">G2</font> =  <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Maroon" title="c1">f</font>;<br/>
<b>set </b><font color="Maroon" title="c5">G3</font> =  <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Maroon" title="c2">g</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">f'</font> = <font color="Maroon" title="c1">f</font> as    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of  <a href="grcat_1.html#K8" title="GRCAT_1:func.8">dom</a> <font color="Maroon" title="c1">f</font>, <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Maroon" title="c1">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/>
<b>reconsider </b><font color="Maroon" title="c7">g'</font> = <font color="Maroon" title="c2">g</font> as    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of  <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Maroon" title="c1">f</font>, <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Maroon" title="c2">g</font> <b>by </b><i><a class="txt" href="grcat_1.html#E1:49"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="grcat_1.html#D19" target="_self" title="GRCAT_1:def.19">Def19</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">h'</font> = <font color="Maroon" title="c3">h</font> as    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of  <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Maroon" title="c2">g</font>, <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Maroon" title="c3">h</font> <b>by </b><i><a class="txt" href="grcat_1.html#E1:49"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="grcat_1.html#D19" target="_self" title="GRCAT_1:def.19">Def19</a></i>;<br/>
<a NAME="E5:49"/>
<font color="Maroon" title="c8">h'</font> <a href="grcat_1.html#K15" title="GRCAT_1:func.15">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g'</font> <a href="grcat_1.html#K15" title="GRCAT_1:func.15">*</a> <font color="Maroon" title="c6">f'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">h'</font> <a href="grcat_1.html#K15" title="GRCAT_1:func.15">*</a> <font color="Maroon" title="c7">g'</font></span>)</span> <a href="grcat_1.html#K15" title="GRCAT_1:func.15">*</a> <font color="Maroon" title="c6">f'</font>
 
<b>by </b><i><a class="ref" href="grcat_1.html#T32" target="_self" title="GRCAT_1:th.32">Th32</a></i>;<br/>
<b>hence </b><a NAME="E6:49"/>
<font color="Maroon" title="c3">h</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Maroon" title="c1">f</font>
 ; <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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