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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">h</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="Olive" title="b1">h</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  holds <br/><font color="Maroon" title="c1">G</font>, <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Olive" title="b1">h</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">h</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="c3">h</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  implies <font color="Maroon" title="c1">G</font>, <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a>  )</span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c4">ih</font> = <font color="Maroon" title="c3">h</font> as   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c1">G</font>,<span class="p1">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T49" target="_self" onmouseover="rs('group_6/T49')" onmouseout="rh()">Th49</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:91"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
<font color="Maroon" title="c3">h</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</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="c1">G</font>, <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">h</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c4">ih</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="group_6.html#D11" target="_self" onmouseover="rs('group_6/D11')" onmouseout="rh()">GROUP_6:def 11</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">ih</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> </span><br/>

<a NAME="E3:91"/>
<font color="Maroon" title="c4">ih</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T44" target="_self" onmouseover="rs('group_6/T44')" onmouseout="rh()">Th44</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:91"/>
<font color="Maroon" title="c4">ih</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:91"><span class="lab"><font color="Green" title="E53">A1</font></span></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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