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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> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b3">L1</font>, <font color="Olive" title="b4">L2</font> being    <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b3">L1</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Olive" title="b2">A</font> &amp; <font color="Olive" title="b4">L2</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Olive" title="b2">A</font> holds <br/><font color="Olive" title="b3">L1</font> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</a> <font color="Olive" title="b4">L2</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Olive" title="b2">A</font></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> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font><br/>  for <font color="Olive" title="b2">L1</font>, <font color="Olive" title="b3">L2</font> being    <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b2">L1</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Olive" title="b1">A</font> &amp; <font color="Olive" title="b3">L2</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Olive" title="b1">A</font> holds <br/><font color="Olive" title="b2">L1</font> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</a> <font color="Olive" title="b3">L2</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Olive" title="b1">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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">  for <font color="Olive" title="b1">L1</font>, <font color="Olive" title="b2">L2</font> being    <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">L1</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font> &amp; <font color="Olive" title="b2">L2</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font> holds <br/><font color="Olive" title="b1">L1</font> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</a> <font color="Olive" title="b2">L2</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">L1</font>, <font color="Maroon" title="c5">L2</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="c4">L1</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c5">L2</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font> implies <font color="Maroon" title="c4">L1</font> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</a> <font color="Maroon" title="c5">L2</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font> )</span><br/>









<span class="kw">assume </span><a NAME="E1:46"/>
( <font color="Maroon" title="c4">L1</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c5">L2</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</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="c4">L1</font> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</a> <font color="Maroon" title="c5">L2</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font></span><br/>

<a NAME="E2:46"/><span class="kw">then </span>
(  <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <font color="Maroon" title="c4">L1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> &amp;  <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <font color="Maroon" title="c5">L2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rmod_4.html#D5" target="_self" onmouseover="rs('rmod_4/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<a NAME="E3:46"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A1</font></span>: 
<span class="p1">(<span class="default"><a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <font color="Maroon" title="c4">L1</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <font color="Maroon" title="c5">L2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T8" onmouseover="rs('xboole_1/T8')" onmouseout="rh()">XBOOLE_1:8</a></span>;<br/>
<a NAME="E4:46"/>
 <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L1</font> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</a> <font color="Maroon" title="c5">L2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <font color="Maroon" title="c4">L1</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <font color="Maroon" title="c5">L2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rmod_4.html#T37" target="_self" onmouseover="rs('rmod_4/T37')" onmouseout="rh()">Th37</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:46"/>
 <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L1</font> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</a> <font color="Maroon" title="c5">L2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:46"><span class="lab"><font color="Green" title="E32">A1</font></span></a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="rmod_4.html#D5" target="_self" onmouseover="rs('rmod_4/D5')" onmouseout="rh()">RMOD_4:def 5</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"> verum</span><br/>


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