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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">H1</font>, <font color="Olive" title="b2">H2</font>, <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>  st <span class="p1"><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">[.</a><span class="default"><font color="Olive" title="b1">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="b2">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="b1">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Olive" title="b3">H</font></span>)</span>,<font color="Olive" title="b3">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="b2">H2</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Olive" title="b3">H</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">H1</font>, <font color="Maroon" title="c3">H2</font>, <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"> ( <span class="p1"><a href="grnilp_1.html#K1" title="GRNILP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c2">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="c3">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="c2">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c4">H</font></span>)</span>,<font color="Maroon" title="c4">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="c3">H2</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c4">H</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:16"/><span class="lab"><font color="Green" title="E11">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="c2">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="c3">H2</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"><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="c2">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c4">H</font></span>)</span>,<font color="Maroon" title="c4">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="c3">H2</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c4">H</font></span><br/>

<a NAME="E2:16"/>
<font color="Maroon" title="c2">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c4">H</font> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c4">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T106" title="GROUP_2:th.106">GROUP_2:106</a></span>;<br/>
<a NAME="E3:16"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">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="c2">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c4">H</font></span>)</span>,<font color="Maroon" title="c4">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">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="grnilp_1.html#T12" target="_self" title="GRNILP_1:th.12">Th12</a></span>;<br/>
<a NAME="E4:16"/><span class="lab"><font color="Green" title="E13">A3</font></span>: 
<font color="Maroon" title="c4">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#E15"><span class="lab"><font color="Green" title="E10">Lm2</font></span></a></span>;<br/>
<a NAME="E5:16"/>
<font color="Maroon" title="c2">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c4">H</font> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c2">H1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T106" title="GROUP_2:th.106">GROUP_2:106</a></span>;<br/>
<a NAME="E6:16"/><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="c2">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c4">H</font></span>)</span>,<font color="Maroon" title="c4">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="c2">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="#E4:16"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="ref" href="group_5.html#T75" title="GROUP_5:th.75">GROUP_5:75</a></span>;<br/>
<a NAME="E7:16"/><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="c2">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c4">H</font></span>)</span>,<font color="Maroon" title="c4">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="c3">H2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="group_2.html#T65" title="GROUP_2:th.65">GROUP_2:65</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:16"/>
<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="c2">H1</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c4">H</font></span>)</span>,<font color="Maroon" title="c4">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="c3">H2</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Maroon" title="c4">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="group_2.html#T109" title="GROUP_2:th.109">GROUP_2:109</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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