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<span class="kw">let </span><font color="Maroon" title="c1">G</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">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><br/> for <font color="Olive" title="b3">H</font> being   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> holds <br/> ( <font color="Olive" title="b1">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Olive" title="b3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Olive" title="b3">H</font> iff <font color="Olive" title="b1">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Olive" title="b3">H</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Olive" title="b2">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Olive" title="b3">H</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">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" 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_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> holds <br/> ( <font color="Maroon" title="c2">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Olive" title="b1">H</font> iff <font color="Maroon" title="c2">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Olive" title="b1">H</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Olive" title="b1">H</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">H</font> be    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</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="c2">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font> iff <font color="Maroon" title="c2">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font> )</span><br/>







<a NAME="E1:132"/>
<font color="Maroon" title="c2">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T130" target="_self" title="GROUP_2:th.130">Th130</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:132"/>
( <font color="Maroon" title="c2">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font> implies <font color="Maroon" title="c2">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T66" title="XBOOLE_1:th.66">XBOOLE_1:66</a></span>; <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="c2">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font> implies <font color="Maroon" title="c2">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font> )</span><br/>

<span class="kw">assume </span><a NAME="E3:132"/>
<font color="Maroon" title="c2">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</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="c2">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E5:132"/><span class="lab"><font color="Green" title="E64">A1</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font>
 <span class="kw">and </span><br/><a NAME="E6:132"/><span class="lab"><font color="Green" title="E65">A2</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">x</font> = <font color="Maroon" title="c5">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:132"><span class="lab"><font color="Green" title="E65">A2</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">g</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><span class="kw"> such that </span><br/><a NAME="E9:132"/><span class="lab"><font color="Green" title="E66">A3</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c7">g</font>
 <span class="kw">and </span><br/><a NAME="E10:132"/><span class="lab"><font color="Green" title="E67">A4</font></span>: 
<font color="Maroon" title="c7">g</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c4">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:132"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="ref" href="group_2.html#T125" target="_self" title="GROUP_2:th.125">Th125</a></span>;<br/>
<a NAME="E11:132"/><span class="lab"><font color="Green" title="E68">A5</font></span>: 
<font color="Maroon" title="c7">g</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c4">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:132"><span class="lab"><font color="Green" title="E67">A4</font></span></a>, <a class="ref" href="group_2.html#T60" target="_self" title="GROUP_2:th.60">Th60</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c8">h</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><span class="kw"> such that </span><br/><a NAME="E13:132"/><span class="lab"><font color="Green" title="E69">A6</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c8">h</font>
 <span class="kw">and </span><br/><a NAME="E14:132"/><span class="lab"><font color="Green" title="E70">A7</font></span>: 
<font color="Maroon" title="c8">h</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c4">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:132"><span class="lab"><font color="Green" title="E65">A2</font></span></a>, <a class="ref" href="group_2.html#T125" target="_self" title="GROUP_2:th.125">Th125</a></span>;<br/>
<font color="Maroon" title="c2">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:132"><span class="lab"><font color="Green" title="E66">A3</font></span></a>, <a class="txt" href="#E13:132"><span class="lab"><font color="Green" title="E69">A6</font></span></a>, <a class="ref" href="group_1.html#T22" title="GROUP_1:th.22">GROUP_1:22</a></span>
<br/>.= 
<font color="Maroon" title="c3">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">h</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></span>
;<br/>
<a NAME="E16:132"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">h</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#T21" title="GROUP_1:th.21">GROUP_1:21</a></span>;<br/>
<a NAME="E17:132"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c4">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:132"><span class="lab"><font color="Green" title="E70">A7</font></span></a>, <a class="txt" href="#E11:132"><span class="lab"><font color="Green" title="E68">A5</font></span></a>, <a class="ref" href="group_2.html#T59" target="_self" title="GROUP_2:th.59">Th59</a></span>;<br/>
<span class="kw">hence </span><a NAME="E18:132"/>
<font color="Maroon" title="c2">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T137" target="_self" title="GROUP_2:th.137">Th137</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/>


</div>
