<?xml version="1.0"?>
<div class="add">

<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">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> holds <br/> ( <font color="Olive" title="b1">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> &amp; <span class="p1">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> )</span><br/><b>let </b><font color="Maroon" title="c2">a</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> &amp; <span class="p1">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> )</span><br/>



<a NAME="E1:104"/>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <span class="p1">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span> &amp;  <a href="group_2.html#K6" title="GROUP_2:func.6">(Omega).</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#G3" title="ALGSTR_0:aggr.3">multMagma</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>,the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">G</font> #) &amp;  <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> &amp; <span class="p1">(<span class="default"><a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font></span>)</span> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> &amp; <font color="Maroon" title="c2">a</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <span class="p1">(<span class="default"><a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> &amp; <font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <span class="p2">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <span class="p2">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c2">a</font> )
 
<b>by </b><i><a class="ref" href="group_2.html#T21" target="_self" title="GROUP_2:th.21">Th21</a></i>;<br/>
<b>hence </b><a NAME="E2:104"/>
( <font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> &amp; <span class="p1">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(Omega).</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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"> verum</span><br/>


</div>
