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<b>let </b><font color="Maroon" title="c1">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">K</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a>  <a href="group_1.html#L1" title="GROUP_1:struct.1">HGrStr</a> ;<br/><b>let </b><font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c4">a2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">K</font>;<br/><b>let </b><font color="Maroon" title="c5">R</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">i</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">K</font>;<br/>







<b>set </b><font color="Maroon" title="c6">F</font> = the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c2">K</font>;<br/>
<b>set </b><font color="Maroon" title="c7">f</font> =  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">K</font>;<br/>
<a NAME="E1:70"/>
the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c2">K</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a>
 
<b>by </b><i><a class="ref" href="group_1.html#T31" title="GROUP_1:th.31">GROUP_1:31</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">a1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c4">a2</font></span>)</span> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Maroon" title="c5">R</font> = 
<span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c2">K</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">[;]</a> <font color="Maroon" title="c3">a1</font>,<span class="p2">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c2">K</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">[;]</a> <font color="Maroon" title="c4">a2</font>,<span class="p3">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">K</font></span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c5">R</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T77" title="FUNCOP_1:th.77">FUNCOP_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c2">K</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">[;]</a> <font color="Maroon" title="c3">a1</font>,<span class="p3">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">K</font></span>)</span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c2">K</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">[;]</a> <font color="Maroon" title="c4">a2</font>,<span class="p3">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">K</font></span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c5">R</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T69" title="FUNCOP_1:th.69">FUNCOP_1:69</a></i>
<br/>.= 
<font color="Maroon" title="c3">a1</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Maroon" title="c5">R</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>
;<br/><br/>


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