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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">H1</font> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b2">H2</font> holds <br/><font color="Olive" title="b1">H1</font> <a href="group_2.html#K9" title="GROUP_2:func.9">/\</a> <font color="Olive" title="b3">H3</font> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b2">H2</font> <a href="group_2.html#K9" title="GROUP_2:func.9">/\</a> <font color="Olive" title="b3">H3</font></span><br/><b>let </b><font color="Maroon" title="c2">H1</font>, <font color="Maroon" title="c3">H2</font>, <font color="Maroon" title="c4">H3</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">H1</font> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c3">H2</font> implies <font color="Maroon" title="c2">H1</font> <a href="group_2.html#K9" title="GROUP_2:func.9">/\</a> <font color="Maroon" title="c4">H3</font> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c3">H2</font> <a href="group_2.html#K9" title="GROUP_2:func.9">/\</a> <font color="Maroon" title="c4">H3</font> )</span><br/>







<b>assume </b><a NAME="E1:94"/>
<font color="Maroon" title="c2">H1</font> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c3">H2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">H1</font> <a href="group_2.html#K9" title="GROUP_2:func.9">/\</a> <font color="Maroon" title="c4">H3</font> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c3">H2</font> <a href="group_2.html#K9" title="GROUP_2:func.9">/\</a> <font color="Maroon" title="c4">H3</font></span><br/>

<a NAME="E2:94"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">H1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">H2</font>
 
<b>by </b><i><a class="ref" href="group_2.html#D5" target="_self" title="GROUP_2:def.5">Def5</a></i>;<br/>
<a NAME="E3:94"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">H1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">H3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">H2</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">H3</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T26" title="XBOOLE_1:th.26">XBOOLE_1:26</a></i>;<br/>
<a NAME="E4:94"/><b>then </b>
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="c2">H1</font> <a href="group_2.html#K9" title="GROUP_2:func.9">/\</a> <font color="Maroon" title="c4">H3</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">H2</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">H3</font>
 
<b>by </b><i><a class="ref" href="group_2.html#T97" target="_self" title="GROUP_2:th.97">Th97</a></i>;<br/>
<a NAME="E5:94"/><b>then </b>
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="c2">H1</font> <a href="group_2.html#K9" title="GROUP_2:func.9">/\</a> <font color="Maroon" title="c4">H3</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> 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">H2</font> <a href="group_2.html#K9" title="GROUP_2:func.9">/\</a> <font color="Maroon" title="c4">H3</font></span>)</span>
 
<b>by </b><i><a class="ref" href="group_2.html#T97" target="_self" title="GROUP_2:th.97">Th97</a></i>;<br/>
<b>hence </b><a NAME="E6:94"/>
<font color="Maroon" title="c2">H1</font> <a href="group_2.html#K9" title="GROUP_2:func.9">/\</a> <font color="Maroon" title="c4">H3</font> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c3">H2</font> <a href="group_2.html#K9" title="GROUP_2:func.9">/\</a> <font color="Maroon" title="c4">H3</font>
 <b>by </b><i><a class="ref" href="group_2.html#T66" target="_self" title="GROUP_2:th.66">Th66</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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