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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font>, <font color="Maroon" title="c3">G3</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"> ( <font color="Maroon" title="c1">G1</font> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c2">G2</font> &amp; <font color="Maroon" title="c2">G2</font> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c3">G3</font> implies <font color="Maroon" title="c1">G1</font> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c3">G3</font> )</span><br/>





<b>assume </b><b>that </b><br/><a NAME="E1:54"/><i><font color="Green" title="E34">A1</font></i>: 
<font color="Maroon" title="c1">G1</font> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c2">G2</font>
 <b>and </b><br/><a NAME="E2:54"/><i><font color="Green" title="E35">A2</font></i>: 
<font color="Maroon" title="c2">G2</font> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c3">G3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">G1</font> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c3">G3</font></span><br/>

<b>set </b><font color="Maroon" title="c4">A</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G1</font>;<br/>
<b>set </b><font color="Maroon" title="c5">B</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">G2</font>;<br/>
<b>set </b><font color="Maroon" title="c6">C</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">G3</font>;<br/>
<b>set </b><font color="Maroon" title="c7">h</font> = the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c3">G3</font>;<br/>
<a NAME="E3:54"/><i><font color="Green" title="E36">A3</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G1</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="c2">G2</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">G2</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">G3</font> )
 
<b>by </b><i><a class="txt" href="group_2.html#E1:54"><i><font color="Green" title="E34">A1</font></i></a>, <a class="txt" href="group_2.html#E2:54"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="group_2.html#D5" target="_self" title="GROUP_2:def.5">Def5</a></i>;<br/>
<a NAME="E4:54"/><b>then </b><i><font color="Green" title="E37">A4</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G1</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">G3</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E5:54"/><i><font color="Green" title="E38">A5</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G1</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">G2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">G2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="txt" href="group_2.html#E3:54"><i><font color="Green" title="E36">A3</font></i></a>, <a class="ref" href="zfmisc_1.html#T119" title="ZFMISC_1:th.119">ZFMISC_1:119</a></i>;<br/>
the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">G1</font> = 
the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c2">G2</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G1</font>
<b>by </b><i><a class="txt" href="group_2.html#E1:54"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="group_2.html#D5" target="_self" title="GROUP_2:def.5">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c3">G3</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">G2</font></span>)</span> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G1</font>
<b>by </b><i><a class="txt" href="group_2.html#E2:54"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="group_2.html#D5" target="_self" title="GROUP_2:def.5">Def5</a></i>
<br/>.= 
the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c3">G3</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G1</font>
<b>by </b><i><a class="txt" href="group_2.html#E5:54"><i><font color="Green" title="E38">A5</font></i></a>, <a class="ref" href="funct_1.html#T82" title="FUNCT_1:th.82">FUNCT_1:82</a></i>
;<br/>
<b>hence </b><a NAME="E7:54"/>
<font color="Maroon" title="c1">G1</font> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c3">G3</font>
 <b>by </b><i><a class="txt" href="group_2.html#E4:54"><i><font color="Green" title="E37">A4</font></i></a>, <a class="ref" href="group_2.html#D5" target="_self" title="GROUP_2:def.5">Def5</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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