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<b>let </b><font color="Maroon" title="c1">R</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/><b>let </b><font color="Maroon" title="c2">V</font> be   <a href="vectsp_2.html#NM7" title="VECTSP_2:NM.7">RightMod</a> of <font color="Maroon" title="c1">R</font>;<br/><b>let </b><font color="Maroon" title="c3">v1</font>, <font color="Maroon" title="c4">v2</font> be   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font>;<br/>







<b>assume </b><a NAME="E1:10"/>
<font color="Maroon" title="c3">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">v2</font>
 ;<br/>

<a NAME="E2:10"/><b>then </b>
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> &amp; <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> &amp;  <a href="rlvect_1.html#K9" title="RLVECT_1:func.9">Sum</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c4">v2</font> )
 
<b>by </b><i><a class="ref" href="finseq_2.html#T147" title="FINSEQ_2:th.147">FINSEQ_2:147</a>, <a class="ref" href="finseq_3.html#T103" title="FINSEQ_3:th.103">FINSEQ_3:103</a>, <a class="ref" href="rlvect_1.html#T62" title="RLVECT_1:th.62">RLVECT_1:62</a></i>;<br/>
<b>hence </b><a NAME="E3:10"/>
 <a href="rmod_4.html#K1" title="RMOD_4:func.1">Sum</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c4">v2</font>
 <b>by </b><i><a class="ref" href="rmod_4.html#D3" target="_self" title="RMOD_4:def.3">Def3</a></i>;<br/>


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