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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></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">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K4">-tuples_on</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>









<b>set </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="fvsum_1.html#K1" target="_self">multfield</a> ;<br/>
<a NAME="E1:72"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="fvsum_1.html#T15" target="_self">Th15</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>3</sub></font> <a href="fvsum_1.html#K10" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="fvsum_1.html#K4" target="_self">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="fvsum_1.html#K1" target="_self">multfield</a> </span>)</span> <a href="finseqop.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="fvsum_1.html#K4" target="_self">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="fvsum_1.html#K1" target="_self">multfield</a> </span>)</span> <a href="finseqop.html#K5">*</a> <span class="p1">(<span class="default">the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>2</sub></font> <a href="finseqop.html#K1">.:</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>

<br/>.= 
the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>2</sub></font> <a href="finseqop.html#K1">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="fvsum_1.html#K1" target="_self">multfield</a> </span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="fvsum_1.html#K1" target="_self">multfield</a> </span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="fvsum_1.html#E1:72"><i><font color="Green">E38</font></i></a>, <a class="ref" href="finseqop.html#T52">FINSEQOP:52</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="fvsum_1.html#K1" target="_self">multfield</a> </span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="fvsum_1.html#K3" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="fvsum_1.html#K1" target="_self">multfield</a> </span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="fvsum_1.html#K10" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="fvsum_1.html#K3" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="fvsum_1.html#K1" target="_self">multfield</a> </span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="fvsum_1.html#K10" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="fvsum_1.html#K4" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="fvsum_1.html#K10" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>

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