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<b>let </b><font color="Maroon" title="c1">K</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="rlvect_1.html#L1" title="RLVECT_1:struct.1">LoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">p1</font>, <font color="Maroon" title="c3">p2</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">K</font>;<br/><b>let </b><font color="Maroon" title="c4">a1</font>, <font color="Maroon" title="c5">a2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font>;<br/><b>let </b><font color="Maroon" title="c6">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>assume </b><b>that </b><br/><a NAME="E1:24"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setwop_2.html#K3" title="SETWOP_2:func.3">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <font color="Maroon" title="c3">p2</font></span>)</span>
 <b>and </b><br/><a NAME="E2:24"/><i><font color="Green" title="E19">A2</font></i>: 
( <font color="Maroon" title="c4">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> &amp; <font color="Maroon" title="c5">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> )
 ;<br/>

<a NAME="E3:24"/>
( <font color="Maroon" title="c2">p1</font> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c1">K</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> <font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c3">p2</font> &amp; <font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setwop_2.html#K3" title="SETWOP_2:func.3">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <font color="Maroon" title="c3">p2</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="fvsum_1.html#E1:24"><i><font color="Green" title="E18">A1</font></i></a></i>;<br/>
<a NAME="E4:24"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <font color="Maroon" title="c3">p2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c1">K</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c5">a2</font>
 
<b>by </b><i><a class="txt" href="fvsum_1.html#E2:24"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="funcop_1.html#T28" title="FUNCOP_1:th.28">FUNCOP_1:28</a></i>;<br/>
<b>hence </b><a NAME="E5:24"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <font color="Maroon" title="c3">p2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a1</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Maroon" title="c5">a2</font>
 ;<br/>


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