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<b>let </b><font color="Maroon" title="c1">O</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">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>  ex <font color="Olive" title="b2">H</font> being <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a> <a href="group_9.html#NM2" title="GROUP_9:NM.2">GroupWithOperators</a> of <font color="Maroon" title="c1">O</font> st <font color="Olive" title="b1">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="Olive" title="b2">H</font>,the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Olive" title="b2">H</font> #)</span><br/><b>let </b><font color="Maroon" title="c2">G</font> be  <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">H</font> being <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a> <a href="group_9.html#NM2" title="GROUP_9:NM.2">GroupWithOperators</a> of <font color="Maroon" title="c1">O</font> st <font color="Maroon" title="c2">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="Olive" title="b1">H</font>,the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Olive" title="b1">H</font> #)</span><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="E2:134"/><i><font color="Green" title="E110">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; <font color="Maroon" title="c2">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="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> #) )
 <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>reconsider </b><font color="Maroon" title="c4">H</font> = <font color="Maroon" title="c3">H</font> as  <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a> <a href="group_9.html#NM2" title="GROUP_9:NM.2">GroupWithOperators</a> of <font color="Maroon" title="c1">O</font> <b>by </b><i><a class="txt" href="#E2:134"><i><font color="Green" title="E110">A1</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">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="c2">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="c4">H</font>,the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c4">H</font> #)</span><br/>

<b>thus </b><a NAME="E4:134"/>
<font color="Maroon" title="c2">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="c4">H</font>,the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c4">H</font> #)
 <b>by </b><i><a class="txt" href="#E2:134"><i><font color="Green" title="E110">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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