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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>, <font color="Maroon">c<sub>4</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>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/>









<a NAME="E1:71"/><i><font color="Green">E38</font></i>: 
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#R6">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#T12" target="_self">Th12</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="fvsum_1.html#K10" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font> = 
<span class="p1">(<span class="default">the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funcop_1.html#K8">[;]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>4</sub></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">c<sub>2</sub></font></span>)</span></span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>5</sub></font>

<br/>.= 
<span class="p1">(<span class="default">the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></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">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></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">c<sub>2</sub></font></span>)</span></span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>5</sub></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">c<sub>2</sub></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">c<sub>2</sub></font> <a href="funcop_1.html#K8">[;]</a> <font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default">the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funcop_1.html#K8">[;]</a> <font color="Maroon">c<sub>4</sub></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">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="fvsum_1.html#E1:71"><i><font color="Green">E38</font></i></a>, <a class="ref" href="finseqop.html#T36">FINSEQOP:36</a></i>
<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">the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funcop_1.html#K8">[;]</a> <font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font></span>)</span></span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funcop_1.html#K8">[;]</a> <font color="Maroon">c<sub>4</sub></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">c<sub>2</sub></font></span>)</span></span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T31">FUNCOP_1:31</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funcop_1.html#K8">[;]</a> <font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font></span>)</span></span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>5</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">the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funcop_1.html#K8">[;]</a> <font color="Maroon">c<sub>4</sub></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">c<sub>2</sub></font></span>)</span></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>5</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">the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funcop_1.html#K8">[;]</a> <font color="Maroon">c<sub>4</sub></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">c<sub>2</sub></font></span>)</span></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>5</sub></font></span>)</span> <a href="fvsum_1.html#K4" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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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