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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">a</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Scalar</a> of <font color="Maroon" title="c1">R</font>;<br/><b>let </b><font color="Maroon" title="c3">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="c4">v</font> be   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c3">V</font>;<br/><b>let </b><font color="Maroon" title="c5">W</font> be    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c3">V</font>;<br/><b>let </b><font color="Maroon" title="c6">w</font> be   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c5">W</font>;<br/>











<b>assume </b><a NAME="E1:15"/><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c6">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c7">ww1</font> = <font color="Maroon" title="c6">w</font> as   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c3">V</font> <b>by </b><i><a class="ref" href="rmod_2.html#T18" target="_self" title="RMOD_2:th.18">Th18</a></i>;<br/>
<a NAME="E3:15"/><i><font color="Green" title="E12">A2</font></i>: 
<font color="Maroon" title="c4">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c3">V</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">ww1</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 
<b>by </b><i><a class="txt" href="rmod_2.html#E1:15"><i><font color="Green" title="E11">A1</font></i></a></i>;<br/>
<a NAME="E4:15"/>
<font color="Maroon" title="c6">w</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c3">V</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">W</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 
<b>by </b><i><a class="ref" href="rmod_2.html#D2" target="_self" title="RMOD_2:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E5:15"/>
<font color="Maroon" title="c6">w</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="txt" href="rmod_2.html#E3:15"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>;<br/>


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