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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">RightModule</a> <font color="Maroon" title="c1">R</font> is  <a href="vectsp_2.html#V4" title="VECTSP_2:attr.4">RightMod-like</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">R</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="vectsp_2.html#D9" target="_self" title="VECTSP_2:def.9">VECTSP_2:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">w</font> being   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp_2.html#K4" title="VECTSP_2:func.4">RightModule</a> <font color="Maroon" title="c1">R</font></span>)</span> holds <br/> ( <span class="p1">(<span class="default"><font color="Olive" title="b1">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b2">w</font></span>)</span> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">w</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c2">x</font></span>)</span> &amp; <font color="Olive" title="b1">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c3">y</font></span>)</span> &amp; <font color="Olive" title="b1">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Olive" title="b1">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">v</font>, <font color="Maroon" title="c5">w</font> be   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp_2.html#K4" title="VECTSP_2:func.4">RightModule</a> <font color="Maroon" title="c1">R</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">w</font></span>)</span> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c2">x</font></span>)</span> &amp; <font color="Maroon" title="c4">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c3">y</font></span>)</span> &amp; <font color="Maroon" title="c4">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c4">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v</font> )</span><br/>





<span class="kw">thus </span><a NAME="E1:59"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">w</font></span>)</span> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c2">x</font></span>)</span> &amp; <font color="Maroon" title="c4">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c3">y</font></span>)</span> &amp; <font color="Maroon" title="c4">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c4">v</font> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_2.html#T24" target="_self" title="VECTSP_2:th.24">Th77</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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