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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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">G</font> being   <a href="group_9.html#NM1" title="GROUP_9:NM.1">GroupWithOperators</a> of <font color="Maroon" title="c1">O</font><br/>  for <font color="Olive" title="b2">H1</font> being    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Olive" title="b1">G</font><br/>  for <font color="Olive" title="b3">H2</font>, <font color="Olive" title="b4">H3</font> being   <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a>   <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Olive" title="b1">G</font>  st <font color="Olive" title="b2">H1</font> is    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Olive" title="b3">H2</font> holds <br/><font color="Olive" title="b2">H1</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <font color="Olive" title="b4">H3</font> is    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Olive" title="b3">H2</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <font color="Olive" title="b4">H3</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">G</font> be   <a href="group_9.html#NM1" title="GROUP_9:NM.1">GroupWithOperators</a> of <font color="Maroon" title="c1">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">H1</font> being    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c2">G</font><br/>  for <font color="Olive" title="b2">H2</font>, <font color="Olive" title="b3">H3</font> being   <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a>   <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c2">G</font>  st <font color="Olive" title="b1">H1</font> is    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Olive" title="b2">H2</font> holds <br/><font color="Olive" title="b1">H1</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <font color="Olive" title="b3">H3</font> is    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Olive" title="b2">H2</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <font color="Olive" title="b3">H3</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">H1</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">H2</font>, <font color="Olive" title="b2">H3</font> being   <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a>   <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c2">G</font>  st <font color="Maroon" title="c3">H1</font> is    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Olive" title="b1">H2</font> holds <br/><font color="Maroon" title="c3">H1</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <font color="Olive" title="b2">H3</font> is    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Olive" title="b1">H2</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <font color="Olive" title="b2">H3</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">H2</font>, <font color="Maroon" title="c5">H3</font> be   <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a>   <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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">H1</font> is    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c4">H2</font> implies <font color="Maroon" title="c3">H1</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <font color="Maroon" title="c5">H3</font> is    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c4">H2</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <font color="Maroon" title="c5">H3</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:110"/>
<font color="Maroon" title="c3">H1</font> is    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c4">H2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">H1</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <font color="Maroon" title="c5">H3</font> is    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c4">H2</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <font color="Maroon" title="c5">H3</font></span><br/>

<a NAME="E2:110"/><span class="kw">then </span>
<font color="Maroon" title="c3">H1</font> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c4">H2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_9.html#D7" target="_self" title="GROUP_9:def.7">Def7</a></span>;<br/>
<a NAME="E3:110"/><span class="kw">then </span>
 <a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c3">H1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c4">H2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#D5" title="GROUP_2:def.5">GROUP_2:def 5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:110"/>
<font color="Maroon" title="c3">H1</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <font color="Maroon" title="c5">H3</font> is    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c4">H2</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <font color="Maroon" title="c5">H3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_9.html#T26" target="_self" title="GROUP_9:th.26">Th26</a>, <a class="ref" href="xboole_1.html#T9" title="XBOOLE_1:th.9">XBOOLE_1:9</a></span>; <a class="txt" 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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