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<span class="kw">let </span><font color="Maroon" title="c1">O</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">G</font> being  <a href="group_9.html#NM2" title="GROUP_9:NM.2">GroupWithOperators</a> of <font color="Maroon" title="c1">O</font><br/> for <font color="Olive" title="b2">H1</font>, <font color="Olive" title="b3">H2</font>, <font color="Olive" title="b4">H3</font> being   <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Olive" title="b1">G</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Olive" title="b3">H2</font></span>)</span> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Olive" title="b4">H3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">H2</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Olive" title="b4">H3</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">G</font> be   <a href="group_9.html#NM2" title="GROUP_9:NM.2">GroupWithOperators</a> of <font color="Maroon" title="c1">O</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>, <font color="Olive" title="b2">H2</font>, <font color="Olive" title="b3">H3</font> being   <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c2">G</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Olive" title="b2">H2</font></span>)</span> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Olive" title="b3">H3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">H2</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Olive" title="b3">H3</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">H1</font>, <font color="Maroon" title="c4">H2</font>, <font color="Maroon" title="c5">H3</font> be    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c2">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">H2</font></span>)</span> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c5">H3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H2</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c5">H3</font></span>)</span></span><br/>









the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">H2</font></span>)</span> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c5">H3</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">H2</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c5">H3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_9.html#D28" target="_self" title="GROUP_9:def.28">Def28</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c3">H1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c4">H2</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c5">H3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_9.html#D28" target="_self" title="GROUP_9:def.28">Def28</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c3">H1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c4">H2</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c5">H3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c3">H1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">H2</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c5">H3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_9.html#D28" target="_self" title="GROUP_9:def.28">Def28</a></span>
<br/>.= 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">H2</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c5">H3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_9.html#D28" target="_self" title="GROUP_9:def.28">Def28</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:80"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">H2</font></span>)</span> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c5">H3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H2</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c5">H3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="group_9.html#E12"><span class="lab"><font color="Green" title="E12">Lm5</font></span></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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