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<b>consider </b><font color="Maroon" title="c2">G</font> being  <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/>
<b>consider </b><font color="Maroon" title="c3">H</font> being  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="group_9.html#L1" title="GROUP_9:struct.1">HGrWOpStr</a> of <font color="Maroon" title="c1">O</font><b> such that </b><br/><a NAME="E3:12_1_1"/><i><font color="Green" title="E9">A1</font></i>: 
( <font color="Maroon" title="c3">H</font> is <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a> &amp; <font color="Maroon" title="c3">H</font> is <a href="group_9.html#V3" title="GROUP_9:attr.3">distributive</a> &amp; <font color="Maroon" title="c3">H</font> is <a href="group_1.html#V2" title="GROUP_1:attr.2">Group-like</a> &amp; <font color="Maroon" title="c3">H</font> is <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a> &amp;  <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="c3">H</font>,the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c3">H</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font> )
 <b>by </b><i><a class="txt" href="group_9.html#E8"><i><font color="Green" title="E8">Lm3</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">H</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">H</font> is <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a> &amp; <font color="Maroon" title="c3">H</font> is <a href="group_9.html#V3" title="GROUP_9:attr.3">distributive</a> &amp; <font color="Maroon" title="c3">H</font> is <a href="group_1.html#V2" title="GROUP_1:attr.2">Group-like</a> &amp; <font color="Maroon" title="c3">H</font> is <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a> )</span><br/>

<b>thus </b><a NAME="E4:12_1_1"/>
( <font color="Maroon" title="c3">H</font> is <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a> &amp; <font color="Maroon" title="c3">H</font> is <a href="group_9.html#V3" title="GROUP_9:attr.3">distributive</a> &amp; <font color="Maroon" title="c3">H</font> is <a href="group_1.html#V2" title="GROUP_1:attr.2">Group-like</a> &amp; <font color="Maroon" title="c3">H</font> is <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a> )
 <b>by </b><i><a class="txt" href="#E3:12_1_1"><i><font color="Green" title="E9">A1</font></i></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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