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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">V</font> being  <a href="vectsp_2.html#NM7" title="VECTSP_2:NM.7">RightMod</a> of <font color="Maroon" title="c1">R</font><br/> for <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">a</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">R</font><br/> for <font color="Olive" title="b4">L</font> being   <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Olive" title="b1">V</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b4">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Olive" title="b3">a</font> <a href="rmod_4.html#R1" title="RMOD_4:pred.1">=</a> <font color="Olive" title="b4">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b3">a</font></span>)</span></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">R</font><br/> for <font color="Olive" title="b3">L</font> being   <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Olive" title="b1">b</font></span>)</span> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Olive" title="b2">a</font> <a href="rmod_4.html#R1" title="RMOD_4:pred.1">=</a> <font color="Olive" title="b3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b2">a</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">a</font> be   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">L</font> being   <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font> <a href="rmod_4.html#R1" title="RMOD_4:pred.1">=</a> <font color="Olive" title="b1">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">a</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c5">L</font> be    <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font> <a href="rmod_4.html#R1" title="RMOD_4:pred.1">=</a> <font color="Maroon" title="c5">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">a</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c6">v</font> be   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="rmod_4.html#D10" target="_self" title="RMOD_4:def.10">RMOD_4:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">a</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">v</font></span><br/>











<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">v</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">v</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">a</font>
<b>by </b><i><a class="ref" href="rmod_4.html#D12" target="_self" title="RMOD_4:def.12">Def12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">v</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">a</font>
<b>by </b><i><a class="ref" href="rmod_4.html#D12" target="_self" title="RMOD_4:def.12">Def12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">v</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">a</font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">a</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">v</font>
<b>by </b><i><a class="ref" href="rmod_4.html#D12" target="_self" title="RMOD_4:def.12">Def12</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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