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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="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</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">  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">A</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font><br/>  for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> holds <br/> ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">a</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">b</font></span>)</span></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Olive" title="b2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b4">b</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Olive" title="b2">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Olive" title="b2">A</font></span>)</span> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">a</font></span>)</span></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">A</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Olive" title="b3">a</font></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <font color="Olive" title="b4">b</font></span>)</span> )</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">  for <font color="Olive" title="b1">A</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> holds <br/> ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">a</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">b</font></span>)</span></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b3">b</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Olive" title="b1">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">a</font></span>)</span></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">A</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Olive" title="b2">a</font></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <font color="Olive" title="b3">b</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">A</font> be   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</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">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> holds <br/> ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">b</font></span>)</span></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font></span>)</span></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <font color="Olive" title="b2">b</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</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"> ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">a</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">b</font></span>)</span></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">b</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">a</font></span>)</span></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c5">a</font></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <font color="Maroon" title="c6">b</font></span>)</span> )</span><br/>







<span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">a</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">b</font></span>)</span></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c4">A</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">b</font></span>)</span></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c4">A</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#D6" onmouseover="rs('group_6/D6')" onmouseout="rh()">GROUP_6:def 6</a></span>
<br/>.= 
<font color="Maroon" title="c3">h</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">b</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">A</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="grsolv_1.html#T13" onmouseover="rs('grsolv_1/T13')" onmouseout="rh()">GRSOLV_1:13</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"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">a</font></span>)</span></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c5">a</font></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <font color="Maroon" title="c6">b</font></span>)</span></span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">a</font></span>)</span></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">b</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">a</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">b</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T107" onmouseover="rs('group_2/T107')" onmouseout="rh()">GROUP_2:107</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">b</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#D6" onmouseover="rs('group_6/D6')" onmouseout="rh()">GROUP_6:def 6</a></span>
<br/>.= 
<font color="Maroon" title="c3">h</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">b</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="grsolv_1.html#T13" onmouseover="rs('grsolv_1/T13')" onmouseout="rh()">GRSOLV_1:13</a></span>
<br/>.= 
<font color="Maroon" title="c3">h</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c5">a</font></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <font color="Maroon" title="c6">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T107" onmouseover="rs('group_2/T107')" onmouseout="rh()">GROUP_2:107</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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