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<b>let </b><font color="Maroon" title="c1">K</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</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"> the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">K</font> is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">K</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">K</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><br/><b>thus </b>the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">K</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> = 
<font color="Maroon" title="c2">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">b</font>

<br/>.= 
<font color="Maroon" title="c3">b</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">a</font>

<br/>.= 
the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">K</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>

; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:3"/>
the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">K</font> is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a>
 <b>by </b><i><a class="ref" href="binop_1.html#D2" title="BINOP_1:def.2">BINOP_1:def 2</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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