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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" 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>, <font color="Olive" title="b2">H1</font>, <font color="Olive" title="b3">H2</font> being    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>  st <span class="p1"><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">[.</a><span class="default"><font color="Olive" title="b2">H1</font>,<span class="p2">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span></span><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">.]</a></span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Olive" title="b3">H2</font> holds <br/><span class="p1"><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Olive" title="b1">H</font></span>)</span>,<font color="Olive" title="b1">H</font></span><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">.]</a></span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Olive" title="b3">H2</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Olive" title="b1">H</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">H</font>, <font color="Maroon" title="c3">H1</font>, <font color="Maroon" title="c4">H2</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" 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"><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">H1</font>,<span class="p2">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span></span><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">.]</a></span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c4">H2</font> implies <span class="p1"><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c2">H</font></span>)</span>,<font color="Maroon" title="c2">H</font></span><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">.]</a></span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c4">H2</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c2">H</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:15"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
<span class="p1"><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">H1</font>,<span class="p2">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span></span><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">.]</a></span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c4">H2</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"><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c2">H</font></span>)</span>,<font color="Maroon" title="c2">H</font></span><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">.]</a></span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c4">H2</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c2">H</font></span><br/>

<a NAME="E2:15"/>
<font color="Maroon" title="c3">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c2">H</font> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c2">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T88" onmouseover="rs('group_2/T88')" onmouseout="rh()">GROUP_2:88</a></span>;<br/>
<a NAME="E3:15"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A2</font></span>: 
<span class="p1"><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c2">H</font></span>)</span>,<font color="Maroon" title="c2">H</font></span><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">.]</a></span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c2">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="grnilp_1.html#T11" target="_self" onmouseover="rs('grnilp_1/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<a NAME="E4:15"/><span class="lab"><font color="Green" title="E12">A3</font></span>: 
<font color="Maroon" title="c2">H</font> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_2.html#K7" title="GROUP_2:func.7">(Omega).</a> <font color="Maroon" title="c1">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="grnilp_1.html#E14"><span class="lab"><font color="Green" title="E9">Lm2</font></span></a></span>;<br/>
<a NAME="E5:15"/>
<font color="Maroon" title="c3">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c2">H</font> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c3">H1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T88" onmouseover="rs('group_2/T88')" onmouseout="rh()">GROUP_2:88</a></span>;<br/>
<a NAME="E6:15"/><span class="kw">then </span>
<span class="p1"><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c2">H</font></span>)</span>,<font color="Maroon" title="c2">H</font></span><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">.]</a></span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <span class="p1"><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">H1</font>,<span class="p2">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span></span><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:15"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="group_5.html#T66" onmouseover="rs('group_5/T66')" onmouseout="rh()">GROUP_5:66</a></span>;<br/>
<a NAME="E7:15"/><span class="kw">then </span>
<span class="p1"><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c2">H</font></span>)</span>,<font color="Maroon" title="c2">H</font></span><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">.]</a></span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c4">H2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="group_2.html#T56" onmouseover="rs('group_2/T56')" onmouseout="rh()">GROUP_2:56</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:15"/>
<span class="p1"><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c2">H</font></span>)</span>,<font color="Maroon" title="c2">H</font></span><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">.]</a></span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c4">H2</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c2">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:15"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="ref" href="group_2.html#T91" onmouseover="rs('group_2/T91')" onmouseout="rh()">GROUP_2:91</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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