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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="Red">::  thesis: </font></span></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">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="Olive" title="b1">V</font> holds   <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">L1</font> <a href="rmod_4.html#K9" title="RMOD_4:func.9">-</a> <font color="Olive" title="b3">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="Olive" title="b2">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="Olive" title="b3">L2</font></span>)</span></span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  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> holds   <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">L1</font> <a href="rmod_4.html#K9" title="RMOD_4:func.9">-</a> <font color="Olive" title="b2">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="Olive" title="b1">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="Olive" title="b2">L2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">L1</font>, <font color="Maroon" title="c4">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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="rmod_4.html#K9" title="RMOD_4:func.9">-</a> <font color="Maroon" title="c4">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="c3">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="c4">L2</font></span>)</span></span><br/>







<a NAME="E1:84"/>
 <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="rmod_4.html#K9" title="RMOD_4:func.9">-</a> <font color="Maroon" title="c4">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="c3">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> <span class="p2">(<span class="default"><a href="rmod_4.html#K8" title="RMOD_4:func.8">-</a> <font color="Maroon" title="c4">L2</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rmod_4.html#T51" target="_self" title="RMOD_4:th.51">Th51</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:84"/>
 <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="rmod_4.html#K9" title="RMOD_4:func.9">-</a> <font color="Maroon" title="c4">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="c3">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="c4">L2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rmod_4.html#T69" target="_self" title="RMOD_4:th.69">Th69</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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