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<span class="kw">let </span><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">H</font>, <font color="Maroon" title="c3">I</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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><br/> for <font color="Olive" title="b2">h1</font> being  <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c3">I</font>  st <font color="Olive" title="b1">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  &amp; <font color="Olive" title="b2">h1</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  holds <br/><font color="Olive" title="b2">h1</font> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <font color="Olive" title="b1">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">h1</font> being  <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c3">I</font>  st <font color="Maroon" title="c4">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  &amp; <font color="Olive" title="b1">h1</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  holds <br/><font color="Olive" title="b1">h1</font> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <font color="Maroon" title="c4">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c5">h1</font> be   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c3">I</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="c4">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  &amp; <font color="Maroon" title="c5">h1</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  implies <font color="Maroon" title="c5">h1</font> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <font color="Maroon" title="c4">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:92"/><span class="lab"><font color="Green" title="E54">A1</font></span>: 
<font color="Maroon" title="c4">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> 
 <span class="kw">and </span><br/><a NAME="E2:92"/><span class="lab"><font color="Green" title="E55">A2</font></span>: 
<font color="Maroon" title="c5">h1</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> 
 ; <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="c5">h1</font> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <font color="Maroon" title="c4">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> </span><br/>

<a NAME="E3:92"/>
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c5">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">H</font> &amp;  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">H</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:92"><span class="lab"><font color="Green" title="E54">A1</font></span></a>, <a class="ref" href="group_6.html#T70" target="_self" title="GROUP_6:th.70">Th70</a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">then </span> <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <font color="Maroon" title="c4">h</font></span>)</span> = 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c5">h1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T47" title="RELAT_1:th.47">RELAT_1:47</a></span>
<br/>.= 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">I</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:92"><span class="lab"><font color="Green" title="E55">A2</font></span></a>, <a class="ref" href="group_6.html#T70" target="_self" title="GROUP_6:th.70">Th70</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:92"/>
<font color="Maroon" title="c5">h1</font> <a href="group_6.html#K7" title="GROUP_6:func.7">*</a> <font color="Maroon" title="c4">h</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="#E1:92"><span class="lab"><font color="Green" title="E54">A1</font></span></a>, <a class="txt" href="#E2:92"><span class="lab"><font color="Green" title="E55">A2</font></span></a>, <a class="ref" href="group_6.html#T70" target="_self" title="GROUP_6:th.70">Th70</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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