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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>;<br/><b>let </b><font color="Maroon" title="c2">N2</font> be  <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>;<br/><b>let </b><font color="Maroon" title="c3">N1</font> be  <a href="group_1.html#V1" title="GROUP_1:attr.1">strict</a> <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>;<br/><b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>







<b>assume </b><a NAME="E1:134"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">N1</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c2">N2</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E3:134"/><i><font color="Green" title="E87">A1</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c6">b</font> &amp; <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">N1</font> &amp; <font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c2">N2</font> )
 ;<br/>
<a NAME="E4:134"/>
<font color="Maroon" title="c5">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c3">N1</font>
 
<b>by </b><i><a class="txt" href="group_3.html#E3:134"><i><font color="Green" title="E87">A1</font></i></a>, <a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></i>;<br/>
<a NAME="E5:134"/><b>then </b>
<font color="Maroon" title="c5">a</font> <a href="group_3.html#K2" title="GROUP_3:func.2">|^</a> <font color="Maroon" title="c6">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c3">N1</font> <a href="group_3.html#K6" title="GROUP_3:func.6">|^</a> <font color="Maroon" title="c6">b</font>
 
<b>by </b><i><a class="ref" href="group_3.html#T70" target="_self" title="GROUP_3:th.70">Th70</a></i>;<br/>
<a NAME="E6:134"/><b>then </b>
<font color="Maroon" title="c5">a</font> <a href="group_3.html#K2" title="GROUP_3:func.2">|^</a> <font color="Maroon" title="c6">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">N1</font>,the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c3">N1</font> #)
 
<b>by </b><i><a class="ref" href="group_3.html#D13" target="_self" title="GROUP_3:def.13">Def13</a></i>;<br/>
<a NAME="E7:134"/><b>then </b><i><font color="Green" title="E88">A2</font></i>: 
<font color="Maroon" title="c5">a</font> <a href="group_3.html#K2" title="GROUP_3:func.2">|^</a> <font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">N1</font>
 
<b>by </b><i><a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></i>;<br/>
<font color="Maroon" title="c6">b</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="group_3.html#K2" title="GROUP_3:func.2">|^</a> <font color="Maroon" title="c6">b</font></span>)</span> = 
<font color="Maroon" title="c6">b</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c6">b</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
<br/>.= 
<font color="Maroon" title="c5">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c6">b</font>
<b>by </b><i><a class="ref" href="group_3.html#T1" target="_self" title="GROUP_3:th.1">Th1</a></i>
;<br/>
<b>hence </b><a NAME="E9:134"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c2">N2</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">N1</font></span>)</span>
 <b>by </b><i><a class="txt" href="group_3.html#E3:134"><i><font color="Green" title="E87">A1</font></i></a>, <a class="txt" href="group_3.html#E7:134"><i><font color="Green" title="E88">A2</font></i></a></i>;<br/>


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