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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="group_1.html#L1">HGrStr</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">a'</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:65"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="fvsum_1.html#K9" target="_self">*</a> <font color="Maroon">p</font></span>)</span>
 <b>and </b><br/><a NAME="E2:65"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">a'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 ;<br/>

<a NAME="E3:65"/><i><font color="Green">E81</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="fvsum_1.html#K9" target="_self">*</a> <font color="Maroon">p</font></span>)</span> &amp; <font color="Maroon">a</font> <a href="fvsum_1.html#K9" target="_self">*</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <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> <font color="Maroon">a</font>,<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">p</font> )
 
<b>by </b><i><a class="ref" href="fvsum_1.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E4:65"/><b>then </b><i><font color="Green">E82</font></i>: 
<font color="Maroon">a'</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <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> <font color="Maroon">a</font>,<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>
 
<b>by </b><i><a class="ref" href="fvsum_1.html#T9" target="_self">Th9</a>, <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="fvsum_1.html#K9" target="_self">*</a> <font color="Maroon">p</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</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> <font color="Maroon">a</font>,<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="funct_2.html#K3">.</a> <font color="Maroon">a'</font>
<b>by </b><i><a class="ref" href="fvsum_1.html#T9" target="_self">Th9</a>, <a class="ref" href="fvsum_1.html#T10" target="_self">Th10</a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>
<br/>.= 
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">K</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><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> <a href="funct_2.html#K3">.</a> <font color="Maroon">a'</font></span>)</span>
<b>by </b><i><a class="ref" href="fvsum_1.html#T11" target="_self">Th11</a>, <a class="ref" href="funcop_1.html#T42">FUNCOP_1:42</a></i>
<br/>.= 
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">K</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">a'</font>
<b>by </b><i><a class="ref" href="funct_1.html#T35">FUNCT_1:35</a></i>
<br/>.= 
<font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a'</font>
<b>by </b><i><a class="ref" href="group_1.html#D1">GROUP_1:def 1</a></i>
;<br/>


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