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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">a1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font>;<br/><b>let </b><font color="Maroon">a2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font>;<br/><b>let </b><font color="Maroon">R</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/>









<a NAME="E1:71"/><i><font color="Green">E48</font></i>: 
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">K</font> <a href="binop_1.html#R6">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><span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">a2</font></span>)</span> <a href="fvsum_1.html#K10" target="_self">*</a> <font color="Maroon">R</font> = 
<span class="p1">(<span class="default">the <a href="group_1.html#U1">mult</a> of <font color="Maroon">K</font> <a href="funcop_1.html#K8">[;]</a> <span class="p2">(<span class="default">the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">K</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">a1</font>,<font color="Maroon">a2</font></span>)</span>,<span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font></span>)</span></span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">R</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">K</font> <a href="funcop_1.html#K6">.:</a> <span class="p2">(<span class="default">the <a href="group_1.html#U1">mult</a> of <font color="Maroon">K</font> <a href="funcop_1.html#K8">[;]</a> <font color="Maroon">a1</font>,<span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">the <a href="group_1.html#U1">mult</a> of <font color="Maroon">K</font> <a href="funcop_1.html#K8">[;]</a> <font color="Maroon">a2</font>,<span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font></span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">R</font>
<b>by </b><i><a class="ref" href="fvsum_1.html#T9" target="_self">Th9</a>, <a class="ref" href="finseqop.html#T36">FINSEQOP:36</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="fvsum_1.html#K10" target="_self">*</a> <font color="Maroon">R</font></span>)</span> <a href="fvsum_1.html#K4" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="fvsum_1.html#K10" target="_self">*</a> <font color="Maroon">R</font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T31">FUNCOP_1:31</a></i>
;<br/>


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