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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#NM6" title="VECTSP_2:NM.6">RightMod</a> of <font color="Maroon" title="c1">R</font><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">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  <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">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b3">b</font></span>)</span> <a href="rmod_4.html#R1" title="RMOD_4:pred.1">=</a> <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">a</font></span>)</span> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</a> <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="b3">b</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be   <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">RightMod</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">a</font>, <font color="Olive" title="b2">b</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">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  <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">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="rmod_4.html#R1" title="RMOD_4:pred.1">=</a> <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">a</font></span>)</span> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</a> <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="b2">b</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</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">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  <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">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="rmod_4.html#R1" title="RMOD_4:pred.1">=</a> <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">a</font></span>)</span> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</a> <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="c4">b</font></span>)</span></span><br/><span class="kw">let </span><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" 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"> <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">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="rmod_4.html#R1" title="RMOD_4: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> <font color="Maroon" title="c3">a</font></span>)</span> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</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> <font color="Maroon" title="c4">b</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">v</font> be   <a href="vectsp_2.html#NM4" title="VECTSP_2:NM.4">Vector</a> of <font color="Maroon" title="c2">V</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="rmod_4.html#D8" target="_self" onmouseover="rs('rmod_4/D8')" onmouseout="rh()">RMOD_4:def 8</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"> <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">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c4">b</font></span>)</span></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"><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">a</font></span>)</span> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</a> <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="c4">b</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/>











<span class="kw">thus </span><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">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c4">b</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 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">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c4">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rmod_4.html#D10" target="_self" onmouseover="rs('rmod_4/D10')" onmouseout="rh()">Def10</a></span>
<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">a</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <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="c4">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D7" onmouseover="rs('vectsp_1/D7')" onmouseout="rh()">VECTSP_1:def 7</a></span>
<br/>.= 
<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">a</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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <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="c4">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rmod_4.html#D10" target="_self" onmouseover="rs('rmod_4/D10')" onmouseout="rh()">Def10</a></span>
<br/>.= 
<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">a</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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <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="c4">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rmod_4.html#D10" target="_self" onmouseover="rs('rmod_4/D10')" onmouseout="rh()">Def10</a></span>
<br/>.= 
<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">a</font></span>)</span> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</a> <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="c4">b</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 class="kw">by</span> <span class="lab"><a class="ref" href="rmod_4.html#D9" target="_self" onmouseover="rs('rmod_4/D9')" onmouseout="rh()">Def9</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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