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<span class="kw">let </span><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">H</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">g</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font>  st <font color="Maroon" title="c1">G</font> is   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a> holds <br/> <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Olive" title="b1">g</font> is  <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">g</font> be   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">G</font> is   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a> implies  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">g</font> is  <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  )</span><br/>





<span class="kw">assume </span><a NAME="E1:74"/><span class="lab"><font color="Green" title="E42">A1</font></span>: 
<font color="Maroon" title="c1">G</font> is   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">g</font> is  <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">h1</font>, <font color="Maroon" title="c5">h2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">g</font></span>)</span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="group_1.html#D12" onmouseover="rs('group_1/D12')" onmouseout="rh()">GROUP_1:def 12</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">h1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">h1</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c6">c</font> = <font color="Maroon" title="c4">h1</font>, <font color="Maroon" title="c7">d</font> = <font color="Maroon" title="c5">h2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">H</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T42" onmouseover="rs('group_2/T42')" onmouseout="rh()">GROUP_2:42</a></span>;<br/>
<a NAME="E3:74"/>
<font color="Maroon" title="c4">h1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">g</font>
 
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><span class="kw"> such that </span><br/><a NAME="E5:74"/><span class="lab"><font color="Green" title="E43">A2</font></span>: 
<font color="Maroon" title="c4">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T45" target="_self" onmouseover="rs('group_6/T45')" onmouseout="rh()">Th45</a></span>;<br/>
<a NAME="E6:74"/>
<font color="Maroon" title="c5">h2</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">g</font>
 
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><span class="kw"> such that </span><br/><a NAME="E8:74"/><span class="lab"><font color="Green" title="E44">A3</font></span>: 
<font color="Maroon" title="c5">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T45" target="_self" onmouseover="rs('group_6/T45')" onmouseout="rh()">Th45</a></span>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c4">h1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">h2</font> = 
<font color="Maroon" title="c6">c</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T43" onmouseover="rs('group_2/T43')" onmouseout="rh()">GROUP_2:43</a></span>
<br/>.= 
<font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c9">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:74"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="txt" href="#E8:74"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="group_6.html#D6" target="_self" onmouseover="rs('group_6/D6')" onmouseout="rh()">Def6</a></span>
<br/>.= 
<font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c8">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="txt" href="group_6.html#E62"><span class="lab"><font color="Green" title="E41">Lm2</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c7">d</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">c</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:74"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="txt" href="#E8:74"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="group_6.html#D6" target="_self" onmouseover="rs('group_6/D6')" onmouseout="rh()">Def6</a></span>
<br/>.= 
<font color="Maroon" title="c5">h2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">h1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T43" onmouseover="rs('group_2/T43')" onmouseout="rh()">GROUP_2:43</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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