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<b>let </b><font color="Maroon" title="c1">G</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</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#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">G</font><br/> for <font color="Olive" title="b2">g</font>, <font color="Olive" title="b3">h</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>  st <font color="Maroon" title="c1">G</font> is <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b2">g</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b3">h</font></span>)</span> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">h</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <font color="Olive" title="b1">A</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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"> for <font color="Olive" title="b1">g</font>, <font color="Olive" title="b2">h</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>  st <font color="Maroon" title="c1">G</font> is <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">g</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b2">h</font></span>)</span> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">h</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <font color="Maroon" title="c2">A</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">g</font>, <font color="Maroon" title="c4">h</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="c1">G</font> is <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">h</font></span>)</span> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <font color="Maroon" title="c2">A</font></span>)</span> )</span><br/>







<b>assume </b><a NAME="E1:29"/><i><font color="Green" title="E16">A1</font></i>: 
<font color="Maroon" title="c1">G</font> is <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">h</font></span>)</span> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <font color="Maroon" title="c2">A</font></span>)</span></span><br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">h</font></span>)</span> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <font color="Maroon" title="c2">A</font> = 
<span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">g</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">h</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Maroon" title="c2">A</font>
<b>by </b><i><a class="ref" href="group_2.html#T22" target="_self" title="GROUP_2:th.22">Th22</a></i>
<br/>.= 
<font color="Maroon" title="c3">g</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <font color="Maroon" title="c2">A</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:29"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="group_2.html#T14" target="_self" title="GROUP_2:th.14">Th14</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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