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<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">K</font> be  non <a href="struct_0.html#V3">empty</a> <a href="vectsp_1.html#V7">distributive</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font>;<br/><b>let </b><font color="Maroon">R1</font> be    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">i</font> <a href="finseq_2.html#K4">-tuples_on</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font>;<br/><b>let </b><font color="Maroon">R2</font> be    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">i</font> <a href="finseq_2.html#K4">-tuples_on</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font>;<br/>









<b>set </b><font color="Maroon">aM</font> = <font color="Maroon">a</font> <a href="fvsum_1.html#K1" target="_self">multfield</a> ;<br/>
<a NAME="E1:72"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">a</font> <a href="fvsum_1.html#K1" target="_self">multfield</a>  <a href="binop_1.html#R7">is_distributive_wrt</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">K</font>
 
<b>by </b><i/>;<br/>
<b>thus </b><a NAME="E2:72"/>
<font color="Maroon">a</font> <a href="fvsum_1.html#K10" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">R1</font> <a href="fvsum_1.html#K4" target="_self">+</a> <font color="Maroon">R2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="fvsum_1.html#K10" target="_self">*</a> <font color="Maroon">R1</font></span>)</span> <a href="fvsum_1.html#K4" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="fvsum_1.html#K10" target="_self">*</a> <font color="Maroon">R2</font></span>)</span>
 <b>by </b><i><a class="ref" href="fvsum_1.html#T9" target="_self">Th9</a>, <a class="ref" href="finseqop.html#T52">FINSEQOP:52</a></i>;<br/>


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