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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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> being   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Maroon" title="c1">R</font><br/>  for <font color="Olive" title="b2">L1</font>, <font color="Olive" title="b3">L2</font> being    <a href="vectsp_6.html#M1" title="VECTSP_6:mode.1">Linear_Combination</a> of <font color="Olive" title="b1">V</font> holds  <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> (<span class="p2">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Olive" title="b1">V</font></span>)</span>,<font color="Olive" title="b2">L1</font>)</span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> (<span class="p2">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Olive" title="b1">V</font></span>)</span>,<font color="Olive" title="b3">L2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">L1</font> <a href="vectsp_6.html#K8" title="VECTSP_6:func.8">-</a> <font color="Olive" title="b3">L2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">L1</font>, <font color="Olive" title="b2">L2</font> being    <a href="vectsp_6.html#M1" title="VECTSP_6:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font> holds  <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> (<span class="p2">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span>,<font color="Olive" title="b1">L1</font>)</span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> (<span class="p2">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span>,<font color="Olive" title="b2">L2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">L1</font> <a href="vectsp_6.html#K8" title="VECTSP_6:func.8">-</a> <font color="Olive" title="b2">L2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">L1</font>, <font color="Maroon" title="c4">L2</font> be    <a href="vectsp_6.html#M1" title="VECTSP_6:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> (<span class="p2">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span>,<font color="Maroon" title="c3">L1</font>)</span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> (<span class="p2">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span>,<font color="Maroon" title="c4">L2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">L1</font> <a href="vectsp_6.html#K8" title="VECTSP_6:func.8">-</a> <font color="Maroon" title="c4">L2</font></span><br/>







<a NAME="E1:41"/>
 <a href="vectsp_6.html#K7" title="VECTSP_6:func.7">-</a> <font color="Maroon" title="c4">L2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zmodul02.html#K11" title="ZMODUL02:func.11">LinComb</a> <font color="Maroon" title="c2">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zmodul02.html#D29" target="_self" onmouseover="rs('zmodul02/D29')" onmouseout="rh()">Def29</a></span>;<br/>
<a NAME="E2:41"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A1</font></span>: 
 <a href="vectsp_6.html#K7" title="VECTSP_6:func.7">-</a> <font color="Maroon" title="c4">L2</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font>
 
;<br/>
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> (<span class="p2">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span>,<font color="Maroon" title="c4">L2</font>)</span>)</span> = 
 <a href="vectsp_6.html#K7" title="VECTSP_6:func.7">-</a> <font color="Maroon" title="c4">L2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="zmodul02.html#T49" target="_self" onmouseover="rs('zmodul02/T49')" onmouseout="rh()">Th49</a></span>
<br/>.= 
 <a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> (<span class="p1">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="vectsp_6.html#K7" title="VECTSP_6:func.7">-</a> <font color="Maroon" title="c4">L2</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:41"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="rlvect_2.html#D1" onmouseover="rs('rlvect_2/D1')" onmouseout="rh()">RLVECT_2:def 1</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:41"/>
<span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> (<span class="p2">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span>,<font color="Maroon" title="c3">L1</font>)</span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> (<span class="p2">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span>,<font color="Maroon" title="c4">L2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">L1</font> <a href="vectsp_6.html#K8" title="VECTSP_6:func.8">-</a> <font color="Maroon" title="c4">L2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zmodul02.html#T47" target="_self" onmouseover="rs('zmodul02/T47')" onmouseout="rh()">Th47</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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